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%I #8 Jul 07 2022 02:19:34
%S 1,1,8,27,864,500,43200,1157625,42875,571536,8001504000,61631955,
%T 10650001824000,8526987612000,13865513485824,91398648466125,
%U 83564478597600,4927753743913000,4421332282230864000,98559233902419862572,340556687709473664000
%N Denominator of Sum_{k=0..n} 1/binomial(n,k)^3.
%H G. C. Greubel, <a href="/A100519/b100519.txt">Table of n, a(n) for n = 0..750</a>
%F a(n) = denominator( 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 Table[Denominator[Sum[1/Binomial[n,k]^3, {k,0,n}]], {n,0,30}] (* _G. C. Greubel_, Jun 24 2022 *)
%o (Magma) [Denominator( (&+[1/Binomial(n,k)^3: k in [0..n]]) ): n in [0..30]]; // _G. C. Greubel_, Jun 24 2022
%o (SageMath) [denominator(sum(1/binomial(n,k)^3 for k in (0..n))) for n in (0..30)] # _G. C. Greubel_, Jun 24 2022
%o (PARI) a(n) = denominator(sum(k=0, n, 1/binomial(n,k)^3)); \\ _Michel Marcus_, Jun 25 2022
%Y Cf. A046825, A100516, A100517, A100518.
%K nonn,frac
%O 0,3
%A _N. J. A. Sloane_, Nov 25 2004
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