A370286 Coefficient of x^n in the expansion of ( (1+x)^3 + x^2 )^n.

1, 3, 17, 102, 645, 4193, 27764, 186231, 1261213, 8604759, 59053167, 407217396, 2819252544, 19583729766, 136426565999, 952743556907, 6667916884701, 46755146944959, 328398159653117, 2310073990369926, 16271915501598595, 114757849228310355

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A002426, A006139.

Cf. A188686, A370287.

Cf. A065065.

Sequence in context: A074565 A339565 A241768 * A054365 A116886 A163064

Adjacent sequences: A370283 A370284 A370285 * A370287 A370288 A370289

Keyword

nonn

Author

Seiichi Manyama, Feb 14 2024

Status

approved