Sorry, I got carried away - the beginning of the 50th diagonal of Pascal's Triangle

Feb 25, 2016

The 50th Diagonal of Pascal’s Triangle: A Sequence Number that generates the terms in the 50th diagonal of Pascal’s triangle, using 12 digit strings, is: 999,999,999,950,000,000,001,224,999,999,980,400,000,000, 230,299,999,997,881,240,000,015,890,699,999,900,115,600, 000,536,878,649,997,494,566,300,010,272,278,169,962,646, 261,200,121,399,651,099,645,139,481,400,937,845,656,297, 749,170,424,884,923,689,695,565,152,620,608,868,053,528, 883,744,594,056,616,847,129,212,243,892,672,553,937,288, 749,815,264,491,956,746,634,521,548,660,036,173,589,393, 562,369,548,660,036,191,956,746,634,488,749,815,264,532, 672,553,937,247,129,212,243,929,594,056,616,818,053,528, 883,765,152,620,608,854,923,689,695,572,749,170,424,880, 937,845,656,299,645,139,481,400,121,399,651,099,962,646, 261,200,010,272,278,169,997,494,566,300,000,536,878,649, 999,900,115,600,000,015,890,699,999,997,881,240,000,000, 230,299,999,999,980,400,000,000,001,224,999,999,999,950, 000,000,000,001. The inverse of this number is: 1/999999999950000000001224999999980400000000230299 99999788124000001589069999990011560000053687864999 74945663000102722781699626462612001213996510996451 39481400937845656297749170424884923689695565152620 60886805352888374459405661684712921224389267255393 72887498152644919567466345215486600361735893935623 69548660036191956746634488749815264532672553937247 12921224392959405661681805352888376515262060885492 36896955727491704248809378456562996451394814001213 99651099962646261200010272278169997494566300000536 87864999990011560000001589069999999788124000000023 02999999999804000000000012249999999999500000000000 01 = 0. 000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000 000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000001  000000000050  000000001275  000000022100  000000292825  000003162510  000028989675  000231917400  001652411475  010648873950  062828356305  .. The first ten non-zero terms in this diagonal are accurately shown above.

David Brooks