A384761 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 A384760.
1, 1, 0, 1, -1, 0, 1, -2, 1, 0, 1, -3, 4, 5, 0, 1, -4, 9, 4, -35, 0, 1, -5, 16, -9, -104, -281, 0, 1, -6, 25, -40, -171, -112, 5671, 0, 1, -7, 36, -95, -176, 717, 14164, 42671, 0, 1, -8, 49, -180, -35, 2176, 20619, -18104, -2179127, 0
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 0, -1, -2, -3, -4, -5, ... 0, 1, 4, 9, 16, 25, ... 0, 5, 4, -9, -40, -95, ... 0, -35, -104, -171, -176, -35, ... 0, -281, -112, 717, 2176, 3875, ...
Programs
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PARI
a(n, k) = if(k==0, 0^n, (-1)^n*k*sum(j=0, n, (n+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+k)^(j-1) * binomial(n,j) * A(n-j,j).