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

Author

N. J. A. Sloane, Nov 25 2004

Keywords

• nonn
• frac

Examples

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

Links

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

Crossrefs

Cf. A046825, A100516, A100517, A100518.

Programs

Magma

[Denominator( (&+[1/Binomial(n,k)^3: k in [0..n]]) ): n in [0..30]]; // G. C. Greubel, Jun 24 2022

Mathematica

Table[Denominator[Sum[1/Binomial[n,k]^3, {k,0,n}]], {n,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

SageMath

[denominator(sum(1/binomial(n,k)^3 for k in (0..n))) for n in (0..30)] # G. C. Greubel, Jun 24 2022

Formula

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