A332539 Denominators of coefficients in a series for log(2 Pi).

2, 4, 24, 432, 120, 8640, 24192, 313600, 2073600, 78382080, 532224000, 2212987392000, 237758976000, 135998134272000, 33798352896000, 28245766348800000, 17072996548608000, 9142589651779584000, 3606419447414784000, 16427702944441958400000, 177473799122780160000

Offset: 0

Author

N. J. A. Sloane, Feb 16 2020

Keywords

• nonn
• frac

Links

• Iaroslav V. Blagouchine and Marc-Antoine Coppo, A note on some constants related to the zeta-function and their relationship with the Gregory coefficients, arXiv:1703.08601 [math.NT], 2017. Also The Ramanujan Journal 47.2 (2018): 457-473. See Cor. 1 to Th. 2.

Crossrefs

Cf. A002206, A002207, A332538.

Cf. A061444 (log(2*Pi)).

Programs

Mathematica

g[n_] := -(-1)^n*Sum[StirlingS1[n, j]/(j + 1), {j, 1, n}]/n!; Flatten[{2, Denominator[Table[Sum[g[k]*g[n + 1 - k], {k, 1, n}]/n, {n, 1, 30}]]}] (* Vaclav Kotesovec, Feb 16 2020 *)

Formula

The reference gives an explicit formula in terms of the Gregory numbers G_n = A002206/A002207.

Extensions

More terms from Vaclav Kotesovec, Feb 16 2020