A369502 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x)^2 ).
1, 6, 47, 420, 4059, 41316, 436345, 4737018, 52535950, 592667532, 6779699073, 78458218746, 916886214115, 10805128064100, 128260666769895, 1532180536574580, 18405744106135914, 222204347510440092, 2694506677864591810, 32804976554127379680, 400837173223351237295
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x)^2)/x) -
PARI
a(n) = sum(k=0, n, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+2,k) * binomial(4*n-2*k+4,n-k).