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 A381566 #12 Feb 28 2025 07:27:36 %S A381566 1,1,0,1,1,0,1,2,1,0,1,3,3,2,0,1,4,6,6,5,0,1,5,10,13,15,16,0,1,6,15, %T A381566 24,33,46,59,0,1,7,21,40,63,99,164,246,0,1,8,28,62,110,188,343,662, %U A381566 1131,0,1,9,36,91,180,331,638,1344,2961,5655,0 %N A381566 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 A087949. %F A381566 See A087949. %e A381566 Square array begins: %e A381566 1, 1, 1, 1, 1, 1, 1, ... %e A381566 0, 1, 2, 3, 4, 5, 6, ... %e A381566 0, 1, 3, 6, 10, 15, 21, ... %e A381566 0, 2, 6, 13, 24, 40, 62, ... %e A381566 0, 5, 15, 33, 63, 110, 180, ... %e A381566 0, 16, 46, 99, 188, 331, 552, ... %e A381566 0, 59, 164, 343, 638, 1110, 1845, ... %o A381566 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n-j+k, j)/(n-j+k)*a(n-j, j))); %Y A381566 Columns k=0..1 give A000007, A087949. %Y A381566 Cf. A379598, A381567, A381569. %K A381566 nonn,tabl %O A381566 0,8 %A A381566 _Seiichi Manyama_, Feb 28 2025