A360314 - OEIS

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A360314

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

1, 0, 0, -2, -2, -2, 4, 10, 16, 2, -32, -86, -90, 26, 332, 646, 534, -690, -3040, -4934, -2270, 9066, 27260, 35198, 532, -101946, -232752, -230730, 158986, 1039078, 1899364, 1265370, -2714160, -9926158, -14625008, -4036358, 34062386, 89744810, 104123084

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

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..38.

FORMULA

G.f.: 1 / sqrt(1+4*x^3/(1-x)).

n*a(n) = 2*(n-1)*a(n-1) - (n-2)*a(n-2) - 2*(2*n-3)*a(n-3) + 2*(2*n-6)*a(n-4).

PROG

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n-1-2*k, n-3*k)*binomial(2*k, k));

(PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1+4*x^3/(1-x)))

CROSSREFS