A370217 Coefficient of x^n in the expansion of ( (1+x)^2 / (1-x^3)^3 )^n.

1, 2, 6, 29, 166, 927, 5055, 27687, 153702, 861950, 4862481, 27543111, 156571951, 892919445, 5106591405, 29275176204, 168181755750, 967967551701, 5580293663274, 32217589171489, 186253647533841, 1078046039503182, 6246592211179337, 36231065957573793

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(2*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)^2 * (1-x^3)^3 ). See A369402.

Prog

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

Crossrefs

Cf. A369402.

Sequence in context: A372372 A107375 A302863 * A020126 A124529 A370456

Adjacent sequences: A370214 A370215 A370216 * A370218 A370219 A370220

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2024

Status

approved