A174461 G.f.: exp( Sum_{n>=1} A174462(n)*x^n/n ) where A174462(n) = Sum_{d|n} C(n,d)^2.

1, 1, 3, 6, 21, 32, 174, 236, 1310, 2609, 12579, 18150, 150980, 198821, 1471346, 2645433, 17956158, 24534384, 234506155, 304507520, 2773986000, 4315363549, 36311714888, 47769153478, 500399410005, 637747787407, 6468558255893, 9142971548460, 88936892205131

Offset

0,3

Comments

Compare to the g.f. G(x) of the Catalan numbers:

G(x)^2 = exp( Sum_{n>=1} A000984(n)*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1671

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, x^m/m*sumdiv(m, d, binomial(m, d)^2))+x*O(x^n)), n)}

Crossrefs

Cf. A174462, A110448.

Sequence in context: A210504 A101582 A069558 * A050611 A270510 A300891

Adjacent sequences: A174458 A174459 A174460 * A174462 A174463 A174464

Keyword

nonn

Author

Paul D. Hanna, Apr 04 2010

Status

approved