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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(3*n-k+3,n-3*k).
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^3)^2))/x)
1, 3, 12, 57, 301, 1700, 10045, 61303, 383335, 2443113, 15811317, 103627692, 686402602, 4587643765, 30900426417, 209539509967, 1429344492215, 9801262309209, 67523359213569, 467136798336153, 3243948604314619, 22604271635042853, 158001453530915361
<a href="/index/Res#revert">Index entries for reversions of series</a>
(PARI) a(n, s=3, t=2, u=1) = 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) * (1+x+x^3)^2) ).
1, 3, 12, 57, 301, 1700, 10045, 61303, 383335, 2443113, 15811317, 103627692, 686402602, 4587643765, 30900426417, 209539509967, 1429344492215, 9801262309209
0,2
allocated
nonn
Seiichi Manyama, Jan 23 2024
approved
editing