A369479 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^2)^3) ).
1, 4, 25, 185, 1503, 12958, 116410, 1077872, 10213954, 98574454, 965545161, 9574235477, 95920415338, 969467658540, 9872949735243, 101211280459929, 1043597450013094, 10816134194658976, 112617367970103163, 1177413807406659659, 12355753915291229596
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^2)^3))/x) -
PARI
a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(4*n-k+4,n-2*k).