A368964 Expansion of (1/x) * Series_Reversion( x * (1-x-x^3)^3 ).
1, 3, 15, 94, 660, 4959, 38995, 316875, 2639754, 22423292, 193484208, 1691190228, 14942632450, 133242614565, 1197520200870, 10836727044255, 98656011543816, 902936341411170, 8303218554134769, 76679352910367832, 710839322080978272, 6612557820697157410
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)^3)/x) -
PARI
a(n, s=3, t=3, 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(3*n+k+2,k) * binomial(4*n-2*k+2,n-3*k).