A112501 Row sums of triangle A112500.

1, 2, 6, 23, 108, 601, 3874, 28448, 234903, 2158498, 21883451, 243025718, 2938265815, 38469994687, 542905969228, 8224586470983, 133260591917731, 2301776455966976, 42258406133001866, 822404997883448574

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=1..n+1} A112500(n, k), n >= 0.

G.f: Sum_{n>=1} x^(n-1)/(Product_{k=1..n} (1 - k*x)^(n-k+1)). - Paul D. Hanna, Feb 16 2010

Example

Contribution from Paul D. Hanna, Feb 16 2010: (Start)
G.f. A(x) = 1 + 2*x + 6*x^2 + 23*x^3 + 108*x^4 + 601*x^5 + ...
A(x) = 1/(1-x) + x/[(1-x)^2*(1-2x)] + x^2/[(1-x)^3*(1-2x)^2*(1-3x)] + ... (End)

Prog

(PARI) {a(n)=polcoeff(sum(m=1, 16, x^(m-1)/prod(k=1, m, (1-k*x +x*O(x^n))^(m-k+1))), n)} \\ Paul D. Hanna, Feb 16 2010

Crossrefs

Sequence in context: A155857 A071076 A297196 * A093345 A289681 A002136

Adjacent sequences: A112498 A112499 A112500 * A112502 A112503 A112504

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 14 2005

Status

approved