A124380 O.g.f.: A(x) = Sum_{n>=0} x^n*Product_{k=0..n} (1 + k*x).

1, 1, 2, 4, 9, 22, 57, 157, 453, 1368, 4296, 13995, 47138, 163779, 585741, 2152349, 8113188, 31326760, 123748871, 499539900, 2058542819, 8651755865, 37054078481, 161591063250, 717032333816, 3235298221401, 14834735654080, 69085973044125

Offset

0,3

Comments

The Kn11 triangle sums of A094638 are given by the terms of this sequence. For the definitions of this and other triangle sums see A180662. [From Johannes W. Meijer, Apr 20 2011]

Links

Table of n, a(n) for n=0..27.

Formula

O.g.f.: A(x) = 1 + x*(1+x)/(G(0) - x*(1+x)) ; G(k) = 1+x*(k*x+x+1) - x*(k*x + 2*x + 1)/G(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 02 2011

G.f.: (G(0) - 1)/(x-1) where G(k) = 1 - (1+x*k)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 16 2013

G.f.: 1/(x*Q(0)-1)/x^4 + (1+x-x^3)/x^4, where Q(k)= 1 - x/(1 - (k+1)*x - x*(k+1)/(x - 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 19 2013

Example

A(x) = 1 + x*(1+x) + x^2*(1+x)*(1+2x) + x^3*(1+x)*(1+2x)*(1+3x) +...

Prog

(PARI) a(n)=polcoeff(sum(k=0, n, x^k*prod(j=0, k, 1+j*x+x*O(x^n))), n)

Crossrefs

Sequence in context: A099241 A337067 A249563 * A176084 A192576 A059019

Adjacent sequences: A124377 A124378 A124379 * A124381 A124382 A124383

Keyword

nonn

Author

Paul D. Hanna, Oct 28 2006

Status

approved