A132459 Sums of squared coefficients in the negative powers of the Catalan function: a(n) = Sum_{k=1..n+1} [x^(n-k+1)] 1/C(x^2)^k, where C(x) is the g.f. of A000108.

1, 1, 2, 5, 11, 18, 30, 45, 101, 171, 483, 702, 2745, 3406, 21215, 23237, 202627, 205701, 2169260, 2138431, 24770064, 24197219, 294389605, 286927242, 3600713132, 3508785697, 45050653316, 43916201874, 574363373312

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Prog

(PARI) {a(n)=local(Catalan=2/(1+sqrt(1-4*x^2 +x*O(x^n)))); sum(k=1, n+1, polcoeff(Catalan^-k, n-k+1)^2)}

Crossrefs

Cf. A132461; A000108 (Catalan).

Sequence in context: A298375 A260037 A132455 * A308517 A375714 A101057

Adjacent sequences: A132456 A132457 A132458 * A132460 A132461 A132462

Keyword

nonn

Author

Paul D. Hanna, Aug 21 2007

Status

approved