A384777 - OEIS

A384777

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 A382450.

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 7, 19, 0, 1, 4, 12, 44, 221, 0, 1, 5, 18, 76, 489, 4597, 0, 1, 6, 25, 116, 813, 9750, 174007, 0, 1, 7, 33, 165, 1203, 15543, 358895, 12328367, 0, 1, 8, 42, 224, 1670, 22072, 555696, 25040728, 1674839513, 0, 1, 9, 52, 294, 2226, 29446, 765572, 38156448, 3375603329, 443624694633, 0

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

FORMULA

A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} 2^(n-j) * binomial(n+k,j)/(n+k) * A(n-j,j).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, ...

0, 1, 2, 3, 4, 5, ...

0, 3, 7, 12, 18, 25, ...