A378466 Expansion of (1/x) * Series_Reversion( x * (1 - x - x/(1 - x)^2) ).
1, 2, 10, 63, 444, 3351, 26490, 216523, 1815080, 15519271, 134817972, 1186570526, 10557959696, 94817735251, 858333997230, 7823946906726, 71751021314438, 661541649024816, 6128551736153622, 57018343512420580, 532529776531703666, 4991007108135966433
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x/(1-x)^2))/x) -
PARI
a(n) = sum(k=0, n, binomial(n+k, k)*binomial(2*n+2*k, n-k))/(n+1);
Formula
G.f.: exp( Sum_{k>=1} A378461(k) * x^k/k ).
a(n) = (1/(n+1)) * [x^n] 1/(1 - x - x/(1 - x)^2)^(n+1).
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+k,k) * binomial(2*n+2*k,n-k).