This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253669 #5 Jan 19 2015 04:27:14 %S A253669 0,0,1,0,1,-1,0,1,3,2,0,1,7,-4,-6,0,1,11,26,10,24,0,1,15,74,-46,-36, %T A253669 -120,0,1,19,146,342,144,168,720,0,1,23,242,1066,-756,-624,-960,-5040, %U A253669 0,1,27,362,2414,5944,2844,3408,6480,40320,0,1,31,506,4578,19524 %N A253669 Square array read by ascending antidiagonals, T(n, k) = k!*[x^k](log(x+1)*sum(j=0..n, C(2*n,j)*x^j)), n>=0, k>=0. %F A253669 T(n,n) = A098118(n). %e A253669 Square array starts: %e A253669 [n\k][0 1 2 3 4 5 6] %e A253669 [0] 0, 1, -1, 2, -6, 24, -120, ... %e A253669 [1] 0, 1, 3, -4, 10, -36, 168, ... %e A253669 [2] 0, 1, 7, 26, -46, 144, -624, ... %e A253669 [3] 0, 1, 11, 74, 342, -756, 2844, ... %e A253669 [4] 0, 1, 15, 146, 1066, 5944, -15768, ... %e A253669 [5] 0, 1, 19, 242, 2414, 19524, 127860, ... %e A253669 [6] 0, 1, 23, 362, 4578, 48504, 434568, ... %e A253669 The first few rows as a triangle: %e A253669 0, %e A253669 0, 1, %e A253669 0, 1, -1, %e A253669 0, 1, 3, 2, %e A253669 0, 1, 7, -4, -6, %e A253669 0, 1, 11, 26, 10, 24, %e A253669 0, 1, 15, 74, -46, -36, -120, %e A253669 0, 1, 19, 146, 342, 144, 168, 720. %p A253669 T := (n,k) -> k!*coeff(series(ln(x+1)*add(binomial(2*n,j)*x^j, j=0..n), x, k+1), x, k): for n from 0 to 6 do lprint(seq(T(n,k), k=0..6)) od; %Y A253669 Cf. A098118. %K A253669 sign,tabl %O A253669 0,9 %A A253669 _Peter Luschny_, Jan 18 2015