A368962 Expansion of (1/x) * Series_Reversion( x * (1-x-x^3)^2 ).
1, 2, 7, 32, 165, 910, 5251, 31314, 191463, 1193808, 7561825, 48522630, 314752515, 2060587112, 13597183916, 90342651982, 603886553067, 4058197580308, 27401404029181, 185806213609730, 1264774546754103, 8639226724499070, 59198404680049915
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
- Index entries for reversions of series
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^3)^2)/x) -
PARI
a(n, s=3, t=2, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*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-2*k+1,n-3*k).