A365757 G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^3*A(x)^5).

1, 1, 1, 1, 2, 8, 29, 86, 229, 619, 1836, 5846, 18802, 59356, 185187, 581476, 1855412, 5997965, 19491730, 63395718, 206433172, 674452128, 2213463944, 7293253791, 24098638133, 79791002807, 264698873350, 879945619711, 2931486913728, 9785457123420, 32721317536787

Offset

0,5

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A023432, A212383, A365243, A365756.

Cf. A365695, A365759.

Sequence in context: A365758 A365759 A373905 * A208973 A365761 A100477

Adjacent sequences: A365754 A365755 A365756 * A365758 A365759 A365760

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2023

Status

approved