%I #11 Jul 07 2022 02:19:25
%S 1,2,17,56,1759,1009,86831,2322304,85922,1144667,16019198113,
%T 123357293,21312406359367,17061774340031,27741170437991,
%U 182851619022848,167169857863289,9857517443932187,8844183281912559671,197147246106875452361,681198614358931646209
%N Numerator of Sum_{k=0..n} 1/binomial(n,k)^3.
%H G. C. Greubel, <a href="/A100518/b100518.txt">Table of n, a(n) for n = 0..770</a>
%F a(n) = numerator( Sum_{k=0..n} 1/binomial(n,k)^3 ).
%e 1, 2, 17/8, 56/27, 1759/864, 1009/500, 86831/43200, 2322304/1157625, 85922/42875, 1144667/571536, 16019198113/8001504000, 123357293/61631955, ... = A100518/A100519.
%t Numerator[Table[Sum[1/Binomial[n,k]^3,{k,0,n}],{n,0,20}]] (* _Harvey P. Dale_, Sep 28 2012 *)
%o (Magma) [Numerator( (&+[1/Binomial(n,k)^3: k in [0..n]]) ): n in [0..40]]; // _G. C. Greubel_, Jun 24 2022
%o (SageMath) [numerator(sum(1/binomial(n,k)^3 for k in (0..n))) for n in (0..40)] # _G. C. Greubel_, Jun 24 2022
%o (PARI) a(n) = numerator(sum(k=0, n, 1/binomial(n,k)^3)); \\ _Michel Marcus_, Jun 24 2022
%Y Cf. A046825, A046826, A100516, A100517, A100519.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 25 2004