A372412 Coefficient of x^n in the expansion of ( (1-x+x^2) / (1-x) )^(3*n).

1, 0, 6, 9, 78, 225, 1293, 4851, 24174, 101583, 480531, 2123913, 9869973, 44669742, 206614827, 946394109, 4378019310, 20189406771, 93556141449, 433284753414, 2011960692003, 9345929458455, 43484293732413, 202453490369727, 943647920498997, 4401470801019600

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(n-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)^3 / (1-x+x^2)^3 ). See A369230.

Prog

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

Crossrefs

Cf. A372410, A372411.

Cf. A369230.

Sequence in context: A299917 A204383 A266006 * A103107 A370623 A121233

Adjacent sequences: A372409 A372410 A372411 * A372413 A372414 A372415

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved