A371386 Expansion of (1/x) * Series_Reversion( x * (1-4*x)^2 / (1-x) ).
1, 7, 89, 1391, 24209, 450231, 8759337, 176071263, 3627907745, 76217773799, 1626477863801, 35158334302927, 768222871584817, 16940297062253719, 376507441510456905, 8425543117906277055, 189683436162271517505, 4293057440192560395207
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^2/(1-x))/x) -
PARI
a(n) = sum(k=0, n, 3^k*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(2*n+k+1,k) * binomial(2*n,n-k).