A370216 Coefficient of x^n in the expansion of ( (1+x) / (1-x^3)^3 )^n.

1, 1, 1, 10, 49, 151, 532, 2353, 9745, 37675, 150851, 624603, 2561476, 10426625, 42800031, 176797510, 730069649, 3016004001, 12492387775, 51845882845, 215363387699, 895504027855, 3728271696139, 15538300424315, 64812978200068, 270565786871401, 1130394586039421

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(n,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^3)^3 ). See A369401.

Prog

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

Crossrefs

Cf. A369401.

Sequence in context: A217165 A154066 A056578 * A307904 A226797 A163716

Adjacent sequences: A370213 A370214 A370215 * A370217 A370218 A370219

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2024

Status

approved