A370269 Coefficient of x^n in the expansion of 1/( (1-x) * (1-x^2)^3 )^n.

1, 1, 9, 37, 233, 1251, 7461, 43219, 257769, 1534096, 9224259, 55607850, 336885029, 2046705428, 12472585155, 76185639162, 466380345065, 2860318763352, 17571932737128, 108111252582449, 666049600308483, 4108363051479346, 25369393216077370

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(2*n-2*k-1,n-2*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^2)^3 ). See A365878.

Prog

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

Crossrefs

Cf. A348410, A370103.

Cf. A365878.

Sequence in context: A199894 A232258 A370244 * A026686 A076174 A117085

Adjacent sequences: A370266 A370267 A370268 * A370270 A370271 A370272

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved