A369077 Expansion of (1/x) * Series_Reversion( x * (1+x^3/(1-x))^2 ).
1, 0, 0, -2, -2, -2, 13, 32, 55, -72, -439, -1152, -506, 4870, 20613, 31744, -26392, -313096, -826529, -654362, 3635175, 16431826, 30100349, -15474300, -262654439, -780688624, -756130333, 3013376172, 15711713509, 31584466782, -6090973971, -250819494954
Offset: 0
Keywords
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1+x^3/(1-x))^2)/x) -
PARI
a(n, s=3, t=2, u=-2) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n+k+1,k) * binomial(n-2*k-1,n-3*k).