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reviewed
approved
proposed
reviewed
editing
proposed
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(4*n-k+4,n-3*k).
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x+x^3)^2))/x)
1, 4, 22, 142, 1007, 7590, 59683, 484112, 4021061, 34029532, 292373296, 2543542676, 22360917140, 198341377680, 1772860026933, 15952960500612, 144397901220980, 1313835276189792, 12009823111155481, 110240431974732436, 1015727265740887873
<a href="/index/Res#revert">Index entries for reversions of series</a>
(PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
allocated for Seiichi Manyama
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^3)^2) ).
1, 4, 22, 142, 1007, 7590, 59683, 484112, 4021061, 34029532, 292373296, 2543542676, 22360917140, 198341377680, 1772860026933, 15952960500612
0,2
allocated
nonn
Seiichi Manyama, Jan 23 2024
approved
editing