A369230 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2)^3 ).
1, 0, 3, 3, 24, 54, 283, 900, 4098, 15286, 66555, 268173, 1156951, 4852722, 21007605, 90167059, 393152058, 1712432070, 7524092134, 33112353060, 146518404963, 649861681966, 2893369443183, 12913307575722, 57800647230933, 259298148600504, 1165967972216967
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^2)^3)/x) -
PARI
a(n, s=2, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(n-k-1,n-2*k).