A100519 Denominator of Sum_{k=0..n} 1/binomial(n,k)^3.

1, 1, 8, 27, 864, 500, 43200, 1157625, 42875, 571536, 8001504000, 61631955, 10650001824000, 8526987612000, 13865513485824, 91398648466125, 83564478597600, 4927753743913000, 4421332282230864000, 98559233902419862572, 340556687709473664000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..750

Formula

a(n) = denominator( Sum_{k=0..n} 1/binomial(n,k)^3 ).

Example

1, 2, 17/8, 56/27, 1759/864, 1009/500, 86831/43200, 2322304/1157625, 85922/42875, 1144667/571536, 16019198113/8001504000, 123357293/61631955, ... = A100518/A100519.

Mathematica

Table[Denominator[Sum[1/Binomial[n, k]^3, {k, 0, n}]], {n, 0, 30}] (* G. C. Greubel, Jun 24 2022 *)

Prog

(Magma) [Denominator( (&+[1/Binomial(n, k)^3: k in [0..n]]) ): n in [0..30]]; // G. C. Greubel, Jun 24 2022
(SageMath) [denominator(sum(1/binomial(n, k)^3 for k in (0..n))) for n in (0..30)] # G. C. Greubel, Jun 24 2022
(PARI) a(n) = denominator(sum(k=0, n, 1/binomial(n, k)^3)); \\ Michel Marcus, Jun 25 2022

Crossrefs

Cf. A046825, A100516, A100517, A100518.

Sequence in context: A007235 A029789 A155930 * A272245 A115701 A030483

Adjacent sequences: A100516 A100517 A100518 * A100520 A100521 A100522

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 25 2004

Status

approved