A369262 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^2)^3 ).
1, 1, 5, 17, 80, 363, 1792, 8969, 46319, 242994, 1296046, 6996163, 38175142, 210162728, 1166020560, 6512854409, 36593709385, 206686641555, 1172856064443, 6683348391034, 38228129813288, 219411037878578, 1263245957786120, 7293833100110787, 42224142505632305
Offset: 0
Keywords
Links
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+x^2)^3)/x) -
PARI
a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(2*n-2*k,n-2*k).
a(n) = (1/(n+1)) * [x^n] ( 1/(1-x) * (1+x^2)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024