A370218 Coefficient of x^n in the expansion of ( (1+x)^3 / (1-x^3)^3 )^n.

1, 3, 15, 93, 639, 4578, 33423, 246816, 1838367, 13788399, 104011140, 788315124, 5998380543, 45794787678, 350619595614, 2691082393818, 20699166876831, 159515321712480, 1231354153215123, 9519556856284218, 73694926944160164, 571201080979318470

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(3*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)^3 * (1-x^3)^3 ). See A369403.

Prog

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

Crossrefs

Cf. A369403.

Sequence in context: A193661 A192296 A372374 * A002893 A256335 A258313

Adjacent sequences: A370215 A370216 A370217 * A370219 A370220 A370221

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2024

Status

approved