A100518 Numerator of Sum_{k=0..n} 1/binomial(n,k)^3.

1, 2, 17, 56, 1759, 1009, 86831, 2322304, 85922, 1144667, 16019198113, 123357293, 21312406359367, 17061774340031, 27741170437991, 182851619022848, 167169857863289, 9857517443932187, 8844183281912559671, 197147246106875452361, 681198614358931646209

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..770

Formula

a(n) = numerator( 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

Numerator[Table[Sum[1/Binomial[n, k]^3, {k, 0, n}], {n, 0, 20}]] (* Harvey P. Dale, Sep 28 2012 *)

Prog

(Magma) [Numerator( (&+[1/Binomial(n, k)^3: k in [0..n]]) ): n in [0..40]]; // G. C. Greubel, Jun 24 2022
(SageMath) [numerator(sum(1/binomial(n, k)^3 for k in (0..n))) for n in (0..40)] # G. C. Greubel, Jun 24 2022
(PARI) a(n) = numerator(sum(k=0, n, 1/binomial(n, k)^3)); \\ Michel Marcus, Jun 24 2022

Crossrefs

Cf. A046825, A046826, A100516, A100517, A100519.

Sequence in context: A212836 A338564 A125609 * A367032 A125200 A368390

Adjacent sequences: A100515 A100516 A100517 * A100519 A100520 A100521

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 25 2004

Status

approved