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

Author

Wolfdieter Lang, Oct 14 2005

Keywords

• nonn
• easy

Examples

			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)
		

Programs

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

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