A370244 Coefficient of x^n in the expansion of ( 1/(1-x) * (1+x^2)^3 )^n.

1, 1, 9, 37, 221, 1176, 6759, 38368, 222189, 1290367, 7551534, 44367918, 261789647, 1549582126, 9198837384, 54740021712, 326445873389, 1950448508265, 11673082484595, 69965814023259, 419923664517546, 2523379461715576, 15180084331541402, 91411979525372616

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,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 A369262.

Prog

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

Crossrefs

Cf. A240688, A370243.

Cf. A369262.

Sequence in context: A364700 A199894 A232258 * A370269 A026686 A076174

Adjacent sequences: A370241 A370242 A370243 * A370245 A370246 A370247

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved