A369081 Expansion of (1/x) * Series_Reversion( x * (1+x^3/(1-x))^3 ).
1, 0, 0, -3, -3, -3, 30, 72, 123, -313, -1533, -3888, 827, 28893, 107637, 116372, -420813, -2657823, -5660571, 1544334, 57009453, 190508467, 207797979, -955665852, -5323553041, -11293308333, 6516682923, 125714105729, 411566197974, 382778797437, -2328595584491
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))^3)/x) -
PARI
a(n, s=3, t=3, u=-3) = 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(3*n+k+2,k) * binomial(n-2*k-1,n-3*k).