A371428 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 - x^2) ).
1, 3, 11, 46, 209, 1003, 5002, 25665, 134605, 718371, 3888633, 21298962, 117823660, 657344600, 3694378463, 20896495211, 118865999117, 679545095167, 3902327585407, 22499738052954, 130200110475407, 755927955655813, 4402088019958400, 25706104810367515
Offset: 0
Keywords
Programs
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Mathematica
Table[1/(n+1) Sum[(-1)^k Binomial[n+1,k]Binomial[3n-3k+3,n-2k],{k,0,Floor[n/2]}],{n,0,30}] (* Harvey P. Dale, Sep 25 2024 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3-x^2))/x) -
PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, k)*binomial(3*n-3*k+3, n-2*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+1,k) * binomial(3*n-3*k+3,n-2*k).