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%I #11 Jan 24 2024 05:59:26
%S 1,4,25,185,1503,12958,116410,1077872,10213954,98574454,965545161,
%T 9574235477,95920415338,969467658540,9872949735243,101211280459929,
%U 1043597450013094,10816134194658976,112617367970103163,1177413807406659659,12355753915291229596
%N Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^2)^3) ).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(4*n-k+4,n-2*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^2)^3))/x)
%o (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);
%Y Cf. A106228, A369477.
%Y Cf. A365128, A369480.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 23 2024
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