A368974 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3)^2 ).
1, 3, 15, 89, 580, 4009, 28857, 213967, 1622869, 12531090, 98171544, 778364379, 6233789872, 50355710215, 409790010350, 3356429972859, 27647745771339, 228890532343859, 1903475080613014, 15893483726218904, 133190665385526309, 1119863488613216952
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)*(1-x+x^3)^2)/x) -
PARI
a(n, s=3, t=2, u=1) = sum(k=0, n\s, (-1)^k*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)} (-1)^k * binomial(2*n+k+1,k) * binomial(4*n-2*k+2,n-3*k).