A132459 - OEIS

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.

%I #2 Mar 30 2012 18:37:04

%S 1,1,2,5,11,18,30,45,101,171,483,702,2745,3406,21215,23237,202627,

%T 205701,2169260,2138431,24770064,24197219,294389605,286927242,

%U 3600713132,3508785697,45050653316,43916201874,574363373312

%N 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.

%o (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)}

%Y Cf. A132461; A000108 (Catalan).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 21 2007