A377235 Expansion of 1/(1 - 9*x/(1-x))^(5/3).
1, 15, 195, 2355, 27285, 307833, 3409485, 37253805, 402847620, 4320615390, 46032234486, 487743084150, 5144152999650, 54041442437850, 565803538944450, 5906360704312770, 61495776957754725, 638808193722602175, 6622218378818049075, 68522901145021162275, 707856527414874575805
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-9)^k*binomial(-5/3, k)*binomial(n-1, n-k));
Formula
a(0) = 1; a(n) = 3 * Sum_{k=0..n-1} (5-2*k/n) * a(k).
a(n) = ((11*n+4)*a(n-1) - 10*(n-2)*a(n-2))/n for n > 1.
a(n) = Sum_{k=0..n} (-9)^k * binomial(-5/3,k) * binomial(n-1,n-k).
a(n) ~ Gamma(1/3) * 3^(29/6) * 2^(n - 11/3) * 5^(n - 5/3) * n^(2/3) / Pi. - Vaclav Kotesovec, Oct 21 2024
a(n) = 15*hypergeom([8/3, 1-n], [2], -9) for n > 0. - Stefano Spezia, May 04 2025