A109415 a(n) equals the (n*(n+1)/2)-th partial sum of the self-convolution 4th power of A010054, which has the g.f.: Sum_{k>=0} x^(k*(k+1)/2).

1, 5, 19, 58, 152, 309, 585, 1046, 1666, 2601, 3871, 5508, 7680, 10423, 13835, 17984, 23168, 29225, 36431, 45000, 54780, 66299, 79637, 94546, 111612, 131215, 152683, 177008, 204264, 234375, 267795, 304678, 345240, 389213, 438235, 490842, 548542

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Formula

a(n) = [x^(n*(n+1)/2)] [Sum_{k>=0} x^(k*(k+1)/2)]^4/(1-x).

Prog

(PARI) {a(n)=local(X=x+x*O(x^(n*(n+1)/2))); polcoeff((eta(X^2)^2/eta(X))^4/(1-X), n*(n+1)/2)}

Crossrefs

Cf. A109413, A109414, A010054.

Sequence in context: A202118 A327821 A201082 * A029861 A224034 A107179

Adjacent sequences: A109412 A109413 A109414 * A109416 A109417 A109418

Keyword

nonn

Author

Paul D. Hanna, Jun 27 2005

Status

approved