A369482 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^3)) ).
1, 3, 12, 56, 287, 1564, 8895, 52195, 313655, 1920489, 11938271, 75143016, 477948051, 3067190311, 19835032603, 129129612163, 845603794947, 5566269982581, 36810651063798, 244448822313138, 1629413356387998, 10898124891668031, 73116947514706451
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+x^3)))/x) -
PARI
a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(3*n-k+3,n-3*k).