A369298 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^2 ).
1, 2, 7, 32, 163, 884, 5011, 29342, 176092, 1077384, 6695093, 42140930, 268108170, 1721372836, 11138994028, 72573587520, 475674650717, 3134297846792, 20750020222815, 137953554890508, 920667400056250, 6165565645765092, 41419898169301995
Offset: 0
Keywords
Links
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3)^2)/x) -
PARI
a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-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/3)} binomial(2*n+k+1,k) * binomial(3*n-3*k+1,n-3*k).
a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3)^2 )^(n+1). - Seiichi Manyama, Feb 14 2024