A365759 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^3*A(x)^5).

1, 1, 1, 1, 2, 8, 29, 85, 217, 541, 1471, 4447, 13975, 43103, 129083, 382535, 1147956, 3519462, 10947483, 34162483, 106341406, 330590764, 1030528133, 3229411337, 10170424724, 32127163822, 101633409379, 321862281571, 1020889305476, 3244779281894, 10335256815761

Offset

0,5

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(n+2*k+1,n-3*k) / (n+2*k+1) = Sum_{k=0..floor(n/4)} binomial(n+2*k,6*k) * binomial(6*k,k) / (5*k+1).

Prog

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

Crossrefs

Cf. A364472, A364523, A365760, A365761.

Cf. A365757.

Sequence in context: A365760 A373906 A365758 * A373905 A365757 A378427

Adjacent sequences: A365756 A365757 A365758 * A365760 A365761 A365762

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2023

Status

approved