A365760 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^4*A(x)^5).

1, 1, 1, 1, 1, 2, 8, 29, 85, 211, 469, 1003, 2263, 5734, 15926, 45188, 124730, 330583, 850783, 2175406, 5650746, 15064128, 41006034, 112492472, 307511726, 833907512, 2247908392, 6056190352, 16390505332, 44659671982, 122380777306, 336326321179, 924529751087

Offset

0,6

Links

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

Formula

a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k,k) * binomial(n+k+1,n-4*k) / (n+k+1) = Sum_{k=0..floor(n/5)} binomial(n+k,6*k) * binomial(6*k,k) / (5*k+1).

Prog

(PARI) a(n) = sum(k=0, n\5, binomial(n-4*k, k)*binomial(n+k+1, n-4*k)/(n+k+1));

Crossrefs

Cf. A364472, A364523, A365759, A365761.

Cf. A365758.

Sequence in context: A107025 A212385 A333882 * A373906 A365758 A365759

Adjacent sequences: A365757 A365758 A365759 * A365761 A365762 A365763

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2023

Status

approved