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%I #19 Apr 15 2023 05:03:39
%S 10,34,910,415826,3786350,455594594,226816276970,16546152735874,
%T 4616987879606830,4799607558341375462,674014218452089817870,
%U 339274220304210587466434,5429636257086663655134162970,138634566648793083166951423714
%N Numerators of Glaisher's J-numbers J_n.
%H J. W. L. Glaisher, <a href="https://doi.org/10.1112/plms/s1-31.1.216">On a set of coefficients analogous to the Eulerian numbers</a>, Proc. London Math. Soc., 31 (1899), 216-235.
%H <a href="/index/Ge#Glaisher">Index entries for sequences related to Glaisher's numbers</a>
%e 10/3, 34, 910, 415826/9, 3786350, 455594594, 226816276970/3, 16546152735874, 4616987879606830, ...
%p In := proc(n)
%p 1/(exp(x)+exp(-x)+1) ;
%p coeftayl(%,x=0,2*n) ;
%p %*(2*n)!*(-1)^n*3/2 ;
%p end proc:
%p Jn := proc(n)
%p (2^(2*n+1)+2)*In(n) ;
%p end proc:
%p A260336 := proc(n)
%p numer(Jn(n)) ;
%p end proc: # _R. J. Mathar_, Aug 02 2015
%t GI[n_] := SeriesCoefficient[1/(Exp[x]+Exp[-x]+1), {x, 0, 2n}]*(2n)!*(-1)^n*3/2;
%t GJ[n_] := (2^(2n+1)+2)*GI[n];
%t a[n_] := Numerator[GJ[n]];
%t Table[a[n], {n, 1, 14}] (* _Jean-François Alcover_, Apr 15 2023, after _R. J. Mathar_ *)
%Y Cf. A047789 (denominators).
%K nonn,frac
%O 1,1
%A _N. J. A. Sloane_, Jul 29 2015
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