A366594 G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)^3*A(x)^4.

1, 0, 0, 1, 3, 3, 5, 24, 60, 102, 258, 816, 1992, 4452, 12012, 33617, 84627, 212823, 577361, 1561077, 4063059, 10715009, 29052015, 78235107, 208358693, 560561391, 1522609569, 4120277283, 11129752269, 30240233739, 82441619605, 224488878600, 611770878012

Offset

0,5

Links

Table of n, a(n) for n=0..32.

Formula

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

Prog

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

Crossrefs

Cf. A366272, A366593, A366595.

Cf. A366588, A366591.

Cf. A366557.

Sequence in context: A157241 A365083 A196430 * A265878 A201496 A110426

Adjacent sequences: A366591 A366592 A366593 * A366595 A366596 A366597

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2023

Status

approved