A369440 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x^2)^2) ).
1, 1, 3, 9, 30, 107, 396, 1513, 5915, 23554, 95202, 389555, 1610588, 6717816, 28234064, 119452553, 508330809, 2174393331, 9343913933, 40319400738, 174630125428, 758916134002, 3308320668768, 14462616815619, 63388694309005, 278492994845776, 1226241871745376
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x^2)^2))/x) -
PARI
a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial(u*(n+1), n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(n+1,n-2*k).