A365761 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^2*A(x)^5).

1, 1, 1, 2, 8, 29, 91, 289, 1009, 3706, 13606, 49822, 184726, 696052, 2648746, 10132072, 38952970, 150635860, 585724594, 2287631614, 8968247626, 35281363830, 139256375922, 551306272137, 2188516471579, 8709331962133, 34739262293455, 138863195368540

Offset

0,4

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(n+3*k+1,n-2*k) / (n+3*k+1) = Sum_{k=0..floor(n/3)} binomial(n+3*k,6*k) * binomial(6*k,k) / (5*k+1).

Prog

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

Crossrefs

Cf. A364472, A364523, A365759, A365760.

Cf. A365693.

Sequence in context: A365757 A378427 A208973 * A100477 A302266 A369268

Adjacent sequences: A365758 A365759 A365760 * A365762 A365763 A365764

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2023

Status

approved