A370196 Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x^3) )^n.

1, 2, 6, 23, 102, 477, 2259, 10733, 51174, 245156, 1180381, 5709387, 27723315, 135055845, 659744973, 3230479173, 15850993126, 77918426928, 383646423564, 1891715752242, 9340099603677, 46170434726054, 228479085858447, 1131770152854441, 5611302030239667

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n,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)) ). See A369443.

Prog

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

Crossrefs

Cf. A369443.

Sequence in context: A218225 A279572 A263576 * A370213 A231444 A248900

Adjacent sequences: A370193 A370194 A370195 * A370197 A370198 A370199

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 11 2024

Status

approved