A370246 Coefficient of x^n in the expansion of ( 1/(1-x) * (1+x^3) )^n.

1, 1, 3, 13, 51, 201, 813, 3333, 13779, 57361, 240153, 1010109, 4264989, 18066777, 76745763, 326796213, 1394494803, 5961639969, 25528971369, 109482236013, 470145451401, 2021360463849, 8700225608583, 37484437325157, 161647475666301, 697673760945201

Offset

0,3

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-3*k-1,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^3) ). See A071969.

Prog

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

Crossrefs

Cf. A071969, A370212.

Sequence in context: A101052 A016064 A163774 * A370272 A304629 A301458

Adjacent sequences: A370243 A370244 A370245 * A370247 A370248 A370249

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved