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

Author

Paul D. Hanna, Aug 21 2007

Keywords

• nonn

Crossrefs

Cf. A132461; A000108 (Catalan).

Programs

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)}