A383597 Expansion of 1/( (1-x)^2 * (1-10*x) )^(1/3).
1, 4, 25, 190, 1570, 13552, 120178, 1085620, 9940345, 91962460, 857750233, 8053389142, 76026759760, 721017894640, 6864725124520, 65578937628304, 628320730656586, 6035594205744520, 58110220504754650, 560624083417180300, 5418599393597801020, 52459116546784350880
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
Programs
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Magma
I:=[4,25]; [1] cat [n le 2 select I[n] else ((11*n-7)*Self(n-1) - 10*(n-1) *Self(n-2))/n : n in [1..30]]; // Vincenzo Librandi, May 04 2025
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Mathematica
Table[Sum[(-9)^k *Binomial[-1/3,k]* Binomial[n, k],{k,0,n}],{n,0,25}] (* Vincenzo Librandi, May 04 2025 *) -
PARI
a(n) = sum(k=0, n, (-9)^k*binomial(-1/3, k)*binomial(n, k));
Formula
a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n,k).
n*a(n) = (11*n-7)*a(n-1) - 10*(n-1)*a(n-2) for n > 1.
a(n) ~ 10^(n + 2/3) / (Gamma(1/3) * 3^(4/3) * n^(2/3)). - Vaclav Kotesovec, May 02 2025
a(n) = hypergeom([1/3, -n], [1], -9). - Stefano Spezia, May 04 2025