A371661 G.f. satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x))^2.

1, 4, 64, 1424, 36800, 1036160, 30843648, 954671360, 30415326208, 990831196160, 32853724512256, 1105132250898432, 37620337933582336, 1293586791397064704, 44863864476704768000, 1567543145774827241472, 55125711913212153954304

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..633

Formula

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

Prog

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

Crossrefs

Cf. A271469, A363311, A371660.

Sequence in context: A259272 A361963 A085532 * A352275 A146341 A264335

Adjacent sequences: A371658 A371659 A371660 * A371662 A371663 A371664

Keyword

nonn

Author

Seiichi Manyama, Apr 01 2024

Status

approved