A380178 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 A162659.
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 22, 0, 1, 4, 15, 62, 281, 0, 1, 5, 24, 126, 792, 5396, 0, 1, 6, 35, 220, 1641, 14922, 142297, 0, 1, 7, 48, 350, 2960, 30708, 384316, 4865806, 0, 1, 8, 63, 522, 4905, 55604, 777537, 12836406, 207407489, 0, 1, 9, 80, 742, 7656, 93300, 1393720, 25450806, 535396784, 10710044776, 0
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, 1, ... 0, 1, 2, 3, 4, 5, 6, ... 0, 3, 8, 15, 24, 35, 48, ... 0, 22, 62, 126, 220, 350, 522, ... 0, 281, 792, 1641, 2960, 4905, 7656, ... 0, 5396, 14922, 30708, 55604, 93300, 148446, ... 0, 142297, 384316, 777537, 1393720, 2330305, 3716532, ...
Programs
-
PARI
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
Formula
See A162659.