A377240 Expansion of (1 + 9*x/(1 - 9*x)^(1/3))^(1/3).
1, 3, 0, 45, 108, 1782, 8424, 94527, 596322, 5765904, 41921874, 379715688, 2974945482, 26175549087, 213735748383, 1857916476288, 15539695570341, 134524740926700, 1141825482025200, 9881043227641251, 84668712937125633, 733670610133591773, 6327618171676167195
Offset: 0
Keywords
Crossrefs
Cf. A377239.
Programs
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PARI
a(n) = 9^n*sum(k=0, n, binomial(1/3, k)*binomial(n-2*k/3-1, n-k));
Formula
a(n) = 9^n * Sum_{k=0..n} binomial(1/3,k) * binomial(n-2*k/3-1,n-k).
a(n) ~ 9^n / (Gamma(1/9) * n^(8/9)) * (1 - 2*Gamma(1/9)/(27*Gamma(7/9)*n^(1/3))). - Vaclav Kotesovec, May 03 2025