An algebra problem by Anudeep Reddy

sorry man it took me 4 years and 8 months to look at this comment. I don't know how this went unnoticed. Here is the solution. Have fun

n=100r=0ncr=1 n=100r=1ncr=100 n=100r=2ncr=4950 n=100r=3ncr=161700 n=100r=4ncr=3921225 n=100r=5ncr=75287520 n=100r=6ncr=1192052400 n=100r=7ncr=16007560800 n=100r=8ncr=186087894300 n=100r=9ncr=1902231808400 n=100r=10ncr=17310309456440 n=100r=11ncr=141629804643600 n=100r=12ncr=1050421051106700 n=100r=13ncr=7110542499799200 n=100r=14ncr=44186942677323600 n=100r=15ncr=253338471349988640 n=100r=16ncr=1345860629046814650 n=100r=17ncr=6650134872937201800 n=100r=18ncr=30664510802988208300 n=100r=19ncr=132341572939212267400 n=100r=20ncr=535983370403809682970 n=100r=21ncr=2041841411062132125600 n=100r=22ncr=7332066885177656269200 n=100r=23ncr=24865270306254660391200 n=100r=24ncr=79776075565900368755100 n=100r=25ncr=242519269720337121015504 n=100r=26ncr=699574816500972464467800 n=100r=27ncr=1917353200780443050763600 n=100r=28ncr=4998813702034726525205100 n=100r=29ncr=12410847811948286545336800 n=100r=30ncr=29372339821610944823963760 n=100r=31ncr=66324638306863423796047200 n=100r=32ncr=143012501349174257560226775 n=100r=33ncr=294692427022540894366527900 n=100r=34ncr=580717429720889409486981450 n=100r=35ncr=1095067153187962886461165020 n=100r=36ncr=1977204582144932989443770175 n=100r=37ncr=3420029547493938143902737600 n=100r=38ncr=5670048986634686922786117600 n=100r=39ncr=9013924030034630492634340800 n=100r=40ncr=13746234145802811501267369720 n=100r=41ncr=20116440213369968050635175200 n=100r=42ncr=28258808871162574166368460400 n=100r=43ncr=38116532895986727945334202400 n=100r=44ncr=49378235797073715747364762200 n=100r=45ncr=61448471214136179596720592960 n=100r=46ncr=73470998190814997343905056800 n=100r=47ncr=84413487283064039501507937600 n=100r=48ncr=93206558875049876949581681100 n=100r=49ncr=98913082887808032681188722800 n=100r=50ncr=100891344545564193334812497256 n=100r=51ncr=98913082887808032681188722800 n=100r=52ncr=93206558875049876949581681100 n=100r=53ncr=84413487283064039501507937600 n=100r=54ncr=73470998190814997343905056800 n=100r=55ncr=61448471214136179596720592960 n=100r=56ncr=49378235797073715747364762200 n=100r=57ncr=38116532895986727945334202400 n=100r=58ncr=28258808871162574166368460400 n=100r=59ncr=20116440213369968050635175200 n=100r=60ncr=13746234145802811501267369720 n=100r=61ncr=9013924030034630492634340800 n=100r=62ncr=5670048986634686922786117600 n=100r=63ncr=3420029547493938143902737600 n=100r=64ncr=1977204582144932989443770175 n=100r=65ncr=1095067153187962886461165020 n=100r=66ncr=580717429720889409486981450 n=100r=67ncr=294692427022540894366527900 n=100r=68ncr=143012501349174257560226775 n=100r=69ncr=66324638306863423796047200 n=100r=70ncr=29372339821610944823963760 n=100r=71ncr=12410847811948286545336800 n=100r=72ncr=4998813702034726525205100 n=100r=73ncr=1917353200780443050763600 n=100r=74ncr=699574816500972464467800 n=100r=75ncr=242519269720337121015504 n=100r=76ncr=79776075565900368755100 n=100r=77ncr=24865270306254660391200 n=100r=78ncr=7332066885177656269200 n=100r=79ncr=2041841411062132125600 n=100r=80ncr=535983370403809682970 n=100r=81ncr=132341572939212267400 n=100r=82ncr=30664510802988208300 n=100r=83ncr=6650134872937201800 n=100r=84ncr=1345860629046814650 n=100r=85ncr=253338471349988640 n=100r=86ncr=44186942677323600 n=100r=87ncr=7110542499799200 n=100r=88ncr=1050421051106700 n=100r=89ncr=141629804643600 n=100r=90ncr=17310309456440 n=100r=91ncr=1902231808400 n=100r=92ncr=186087894300 n=100r=93ncr=16007560800 n=100r=94ncr=1192052400 n=100r=95ncr=75287520 n=100r=96ncr=3921225 n=100r=97ncr=161700 n=100r=98ncr=4950 n=100r=99ncr=100 n=100r=100ncr=1 sum=1267650600228229401496703205376

the answer is more simple 2^100.