A370183 Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^3) )^n.

1, 2, 6, 23, 98, 432, 1929, 8689, 39442, 180248, 828376, 3824757, 17727989, 82438852, 384429751, 1797017598, 8417950626, 39506701508, 185718513144, 874346516454, 4121841403488, 19454625634936, 91924347974883, 434783188981384, 2058320844378109, 9752580801216182

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(2*n-k,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)) ). See A369481.

Prog

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

Crossrefs

Cf. A116411, A370184.

Cf. A369481.

Sequence in context: A374165 A150298 A280768 * A278301 A242586 A196018

Adjacent sequences: A370180 A370181 A370182 * A370184 A370185 A370186

Keyword

nonn

Author

Seiichi Manyama, Feb 11 2024

Status

approved