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A100521 Denominator of Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2. 2

%I #9 Jul 07 2022 02:19:50

%S 1,4,72,1200,19600,635040,25613280,82450368,9275666400,595703908800,

%T 2048086772160,23459903026560,413676290035008,4419618483280000,

%U 3221901874311120000,361282596839420256000,2630246784565779288000,9628029406360113091200,1310481780310126504080000

%N Denominator of Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2.

%H G. C. Greubel, <a href="/A100521/b100521.txt">Table of n, a(n) for n = 0..675</a>

%F a(n) = denominator( Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2 ).

%e 1, 7/4, 137/72, 2341/1200, 38629/19600, 1257937/635040, 50881679/25613280, 164078209/82450368, 18480100619/9275666400, 1187779852639/595703908800, ... = A100520/A100521

%t Table[Denominator[Sum[(-1)^k/Binomial[2*n,k]^2, {k,0,2*n}]], {n,0,30}] (* _G. C. Greubel_, Jun 25 2022 *)

%o (Magma) [Denominator( (&+[(-1)^k/Binomial(2*n,k)^2: k in [0..2*n]]) ): n in [0..30]]; // _G. C. Greubel_, Jun 25 2022

%o (SageMath) [denominator(sum((-1)^k/binomial(2*n,k)^2 for k in (0..2*n))) for n in (0..30)] # _G. C. Greubel_, Jun 25 2022

%o (PARI) a(n) = denominator(sum(k=0, 2*n, (-1)^k/binomial(2*n, k)^2)); \\ _Michel Marcus_, Jun 25 2022

%Y Cf. A100520.

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 25 2004

%E Definition corrected by _Alexander Adamchuk_, May 11 2007

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Last modified April 17 11:06 EDT 2024. Contains 371763 sequences. (Running on oeis4.)