A384758 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384757.
1, 1, 0, 1, -1, 0, 1, -2, -1, 0, 1, -3, 0, 14, 0, 1, -4, 3, 34, 9, 0, 1, -5, 8, 54, -88, -1516, 0, 1, -6, 15, 68, -327, -3402, 4345, 0, 1, -7, 24, 70, -720, -4908, 30532, 507870, 0, 1, -8, 35, 54, -1255, -5044, 84321, 1027402, -4984063, 0
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 0, -1, -2, -3, -4, -5, ... 0, -1, 0, 3, 8, 15, ... 0, 14, 34, 54, 68, 70, ... 0, 9, -88, -327, -720, -1255, ... 0, -1516, -3402, -4908, -5044, -2700, ...
Programs
-
PARI
a(n, k) = if(k==0, 0^n, (-1)^n*k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
Formula
A(n,0) = 0^n; A(n,k) = (-1)^n * k * Sum_{j=0..n} (n-j+k)^(j-1) * binomial(n,j) * A(n-j,j).