1+x=1+1*x/(1+x)+1*x^2/(1+x)^4+3*x^3/(1++x)^9+18*x^4/(1+x)^16+172*x^5/(1+1 x)^25+2313*x^6/(1+/x)^36+。。。
还形成三角形行中的最后项,其中行n+1等于行n的部分和,最后项重复2n+1次,从行0中的“1”开始,如图所示:
1;
1, 1, 1;
1, 2, 3, 3, 3, 3, 3;
1, 3, 6, 9, 12, 15, 18, 18, 18, 18, 18, 18, 18;
1, 4, 10, 19, 31, 46, 64, 82, 100, 118, 136, 154, 172, 172, 172, 172, 172, 172, 172, 172, 172;
1, 5, 15, 34, 65, 111, 175, 257, 357, 475, 611, 765, 937, 1109, 1281, 1453, 1625, 1797, 1969, 2141, 2313, 2313, 2313, 2313, 2313, 2313, 2313, 2313, 2313; ...