A372413 Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x) )^n.

1, 0, 0, 3, 4, 5, 21, 49, 92, 237, 595, 1331, 3169, 7787, 18487, 44108, 107036, 258349, 622371, 1508239, 3658679, 8869465, 21543005, 52399612, 127497281, 310487855, 756858661, 1846060464, 4505442967, 11003284052, 26887642756, 65735882819, 160795695676

Offset

0,4

Links

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

Formula

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

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) / (1-x+x^3) ).

Prog

(PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));

Crossrefs

Cf. A372414, A372415.

Cf. A114997.

Sequence in context: A334638 A039573 A037347 * A116474 A208807 A126896

Adjacent sequences: A372410 A372411 A372412 * A372414 A372415 A372416

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved