A332537 Denominators of coefficients in a series for the first Stieltjes constant gamma_1.

2, 6, 32, 432, 207360, 10368000, 48384000, 533433600, 5120962560000, 3687093043200, 6083703521280000, 1472256252149760000, 4019259568368844800000, 64690939719460454400000, 8151058404652017254400000, 1018882300581502156800000, 33256318290980230397952000000

Offset

0,1

Comments

Note the offset here is different from that in A332536 (because A332536(1) would be Pi).

Links

Table of n, a(n) for n=0..16.

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 Th. 1.

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, 6, Denominator[Table[g[n]/n^2 + Sum[g[k]*g[n + 1 - k]*(HarmonicNumber[n] - HarmonicNumber[k])/(n + 1 - k), {k, 1, n - 1}], {n, 2, 20}]]}] (* Vaclav Kotesovec, Feb 16 2020 *)

Crossrefs

Cf. A002206, A002207, A332536.

Sequence in context: A034997 A067735 A326901 * A118077 A013976 A213435

Adjacent sequences: A332534 A332535 A332536 * A332538 A332539 A332540

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2020

Extensions

More terms from Vaclav Kotesovec, Feb 16 2020

Status

approved