A370625 - OEIS

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A370625

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

1, 0, 0, 3, 4, 5, 27, 63, 116, 354, 945, 2123, 5563, 14846, 36519, 93083, 244068, 622013, 1590318, 4131265, 10658969, 27440808, 71127683, 184324461, 476969939, 1237420755, 3213687698, 8343223779, 21682184311, 56400917786, 146742491187, 381991981659

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..31.

FORMULA

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

PROG

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

CROSSREFS

Cf. A054514.