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

0,1

Links

Table of n, a(n) for n=0..20.

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.

Formula

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

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 *)

Crossrefs

Cf. A002206, A002207, A332538.

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

Sequence in context: A081476 A241806 A009273 * A296787 A341633 A128299

Adjacent sequences: A332536 A332537 A332538 * A332540 A332541 A332542

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2020

Extensions

More terms from Vaclav Kotesovec, Feb 16 2020

Status

approved