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%I #9 Jul 07 2022 02:19:42
%S 1,7,137,2341,38629,1257937,50881679,164078209,18480100619,
%T 1187779852639,4086043585673,46823724627623,825926870076593,
%U 8826243587390221,6435629123661395137,721766119107018403553,5255377541226932317019,19239461977895120106181,2618947765106118753941303
%N Numerator of Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2.
%H G. C. Greubel, <a href="/A100520/b100520.txt">Table of n, a(n) for n = 0..675</a>
%F a(n) = numerator( 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[Numerator[Sum[(-1)^k/Binomial[2*n,k]^2, {k,0,2*n}]], {n,0,30}] (* _G. C. Greubel_, Jun 24 2022 *)
%o (Magma) [Numerator( (&+[(-1)^k/Binomial(2*n,k)^2: k in [0..2*n]]) ): n in [0..30]]; // _G. C. Greubel_, Jun 24 2022
%o (SageMath) [numerator(sum((-1)^k/binomial(2*n,k)^2 for k in (0..2*n))) for n in (0..30)] # _G. C. Greubel_, Jun 24 2022
%o (PARI) a(n) = numerator(sum(k=0, 2*n, (-1)^k/binomial(2*n, k)^2)); \\ _Michel Marcus_, Jun 25 2022
%Y Cf. A100516, A100521.
%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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