A364410 - OEIS

A364410

G.f. A(x) satisfies A(x) = 1 + x^2 * (A(x) / (1 - x))^4.

1, 0, 1, 4, 14, 52, 201, 800, 3260, 13536, 57068, 243664, 1051512, 4579088, 20097526, 88810872, 394811696, 1764477304, 7923087616, 35728412152, 161731039076, 734646128920, 3347600839252, 15298276784648, 70097391229500, 321974115549256, 1482242974320685

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(n+2*k-1,n-2*k) * binomial(4*k,k) / (3*k+1).

PROG

(PARI) a(n) = sum(k=0, n\2, binomial(n+2*k-1, n-2*k)*binomial(4*k, k)/(3*k+1));

CROSSREFS

Partial sums give A186996.

Cf. A213336, A366645, A366646.