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 A381602 #14 Jun 04 2025 07:24:15 %S A381602 1,1,0,1,1,0,1,2,4,0,1,3,9,26,0,1,4,15,60,218,0,1,5,22,103,504,2151,0, %T A381602 1,6,30,156,870,4946,23854,0,1,7,39,220,1329,8511,54430,289555,0,1,8, %U A381602 49,296,1895,12988,93070,655362,3783568,0,1,9,60,385,2583,18536,141316,1112382,8496454,52624689,0 %N A381602 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A120971. %F A381602 See A120971. %e A381602 Square array begins: %e A381602 1, 1, 1, 1, 1, 1, 1, ... %e A381602 0, 1, 2, 3, 4, 5, 6, ... %e A381602 0, 4, 9, 15, 22, 30, 39, ... %e A381602 0, 26, 60, 103, 156, 220, 296, ... %e A381602 0, 218, 504, 870, 1329, 1895, 2583, ... %e A381602 0, 2151, 4946, 8511, 12988, 18536, 25332, ... %e A381602 0, 23854, 54430, 93070, 141316, 200930, 273915, ... %o A381602 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n+k, j)/(2*n+k)*a(n-j, 2*j))); %Y A381602 Columns k=0..1 give A000007, A120971, A120970(n+1). %Y A381602 Cf. A379598, A381603. %K A381602 nonn,tabl %O A381602 0,8 %A A381602 _Seiichi Manyama_, Mar 01 2025