A379546 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^3 ) ).
1, 8, 89, 1150, 16190, 240966, 3729185, 59404934, 967608590, 16041857672, 269807678442, 4592326407908, 78954271935856, 1369136489157250, 23918810207745777, 420575805001923782, 7437459126200243030, 132190772588551036800, 2360148586461490077870
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+2*x)^3))/x) -
PARI
a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(n+1, k)*binomial(4*(n+1)-k, n-2*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*(n+1),k) * binomial(2*(n+1),n-k).
a(n) = A371669(n+1)/2 = (1/(n+1)) * Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(n+1,k) * binomial(4*(n+1)-k,n-2*k).
a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 * (1+2*x)^3 )^(n+1).