A109414 a(n) equals the (n*(n+1)/2)-th partial sum of the self-convolution cube of A010054, which has the g.f.: Sum_{k>=0} x^(k*(k+1)/2).

1, 4, 11, 26, 54, 90, 151, 232, 326, 456, 612, 811, 1030, 1304, 1607, 1953, 2383, 2812, 3329, 3893, 4515, 5226, 5983, 6809, 7703, 8718, 9762, 10891, 12160, 13475, 14868, 16380, 17986, 19699, 21524, 23415, 25482, 27658, 29923, 32288, 34814, 37452

Offset

0,2

Links

Table of n, a(n) for n=0..41.

Formula

a(n) = [x^(n*(n+1)/2)] [Sum_{k>=0} x^(k*(k+1)/2)]^3/(1-x).

Prog

(PARI) {a(n)=local(X=x+x*O(x^(n*(n+1)/2))); polcoeff((eta(X^2)^2/eta(X))^3/(1-X), n*(n+1)/2)}

Crossrefs

Cf. A109413, A109415, A010054.

Sequence in context: A002763 A077270 A076048 * A027966 A141534 A320852

Adjacent sequences: A109411 A109412 A109413 * A109415 A109416 A109417

Keyword

nonn

Author

Paul D. Hanna, Jun 27 2005

Status

approved