A260336 - OEIS

%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