A369630 Expansion of (1/x) * Series_Reversion( x * (1/(1+x^3) - x) ).
1, 1, 2, 6, 20, 70, 255, 960, 3707, 14598, 58395, 236626, 969275, 4007041, 16696822, 70053159, 295691622, 1254772103, 5349978803, 22907982780, 98466168572, 424713570017, 1837717336614, 7974744620620, 34698200181696, 151341512079231, 661590732178716
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x^3)-x))/x) -
PARI
a(n) = sum(k=0, n\3, binomial(2*n-3*k+1, k)*binomial(2*n-3*k,n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n-3*k+1,k) * binomial(2*n-3*k,n-3*k).