A370171 - OEIS

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A370171

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

1, 4, 34, 319, 3146, 31929, 330145, 3458620, 36585194, 389893576, 4179819559, 45025583343, 486961123577, 5284324727023, 57508473997848, 627410367071169, 6859805605391466, 75144918246760324, 824558759018846116, 9061483047671168437, 99716283188165243471

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OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..951

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(4*n-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) * (1+x+x^2)^3) ). See A369479.

PROG

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

CROSSREFS

Cf. A370170, A370172.