A365733 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^3).

1, 1, 1, 1, 1, 1, 2, 6, 16, 36, 71, 127, 215, 367, 676, 1376, 2982, 6514, 13855, 28407, 56543, 111127, 219918, 444450, 919744, 1933732, 4082467, 8576027, 17861347, 36938427, 76207797, 157652981, 328119005, 687377565, 1446665765, 3050094661, 6427116181

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

Prog

(PARI) a(n) = sum(k=0, n\6, binomial(n-5*k, k)*binomial(n-2*k+1, n-5*k)/(n-2*k+1));

Crossrefs

Cf. A127902, A186996, A215340, A365079.

Cf. A002293, A365735.

Sequence in context: A254119 A145126 A348289 * A005676 A365735 A365079

Adjacent sequences: A365730 A365731 A365732 * A365734 A365735 A365736

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2023

Status

approved