A260336 Numerators of Glaisher's J-numbers J_n.

10, 34, 910, 415826, 3786350, 455594594, 226816276970, 16546152735874, 4616987879606830, 4799607558341375462, 674014218452089817870, 339274220304210587466434, 5429636257086663655134162970, 138634566648793083166951423714

Offset

1,1

Links

Table of n, a(n) for n=1..14.

J. W. L. Glaisher, On a set of coefficients analogous to the Eulerian numbers, Proc. London Math. Soc., 31 (1899), 216-235.

Index entries for sequences related to Glaisher's numbers

Example

10/3, 34, 910, 415826/9, 3786350, 455594594, 226816276970/3, 16546152735874, 4616987879606830, ...

Maple

In := proc(n)
    1/(exp(x)+exp(-x)+1) ;
    coeftayl(%, x=0, 2*n) ;
    %*(2*n)!*(-1)^n*3/2 ;
end proc:
Jn := proc(n)
    (2^(2*n+1)+2)*In(n) ;
end proc:
A260336 := proc(n)
    numer(Jn(n)) ;
end proc: # R. J. Mathar, Aug 02 2015

Mathematica

GI[n_] := SeriesCoefficient[1/(Exp[x]+Exp[-x]+1), {x, 0, 2n}]*(2n)!*(-1)^n*3/2;
GJ[n_] := (2^(2n+1)+2)*GI[n];
a[n_] := Numerator[GJ[n]];
Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Apr 15 2023, after R. J. Mathar *)

Crossrefs

Cf. A047789 (denominators).

Sequence in context: A272365 A230895 A254674 * A010818 A243939 A065195

Adjacent sequences: A260333 A260334 A260335 * A260337 A260338 A260339

Keyword

nonn,frac

Author

N. J. A. Sloane, Jul 29 2015

Status

approved