A109413 a(n) equals the (n*(n+1)/2)-th partial sum of the self-convolution of A010054, which has the g.f.: Sum_{n>=0} x^(n*(n+1)/2).

1, 3, 6, 11, 17, 24, 35, 45, 58, 71, 87, 106, 123, 144, 164, 189, 216, 240, 269, 298, 329, 365, 396, 437, 471, 510, 551, 591, 642, 683, 730, 778, 827, 882, 932, 987, 1048, 1105, 1165, 1220, 1289, 1355, 1418, 1485, 1549, 1626, 1699, 1772, 1846, 1923, 2002, 2080

Offset

0,2

Links

Table of n, a(n) for n=0..51.

Formula

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

Prog

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

Crossrefs

Cf. A109414, A109415, A010054.

Sequence in context: A025735 A023601 A173143 * A294397 A003022 A025722

Adjacent sequences: A109410 A109411 A109412 * A109414 A109415 A109416

Keyword

nonn

Author

Paul D. Hanna, Jun 27 2005

Status

approved