A369398 Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3) ).
1, 2, 5, 15, 52, 198, 797, 3322, 14195, 61848, 273792, 1228131, 5570200, 25501610, 117694557, 546983631, 2557677780, 12024345942, 56801925455, 269483935384, 1283469626512, 6134259516564, 29412031039568, 141434223863670, 681939435678239, 3296147009539144
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)^2*(1-x^3))/x) -
PARI
a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(2*n+2,n-3*k).
a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 / (1-x^3) )^(n+1). - Seiichi Manyama, Feb 16 2024