A332538 Numerators of coefficients in a series for log(2 Pi).

3, 1, 1, 7, 1, 43, 79, 717, 3481, 100189, 533077, 1777722593, 156155179, 74216302403, 15537618841, 11069240202341, 5762870563187, 2682308717818019, 927089189292457, 3726882116303677517, 35762248102620751, 1529769611935770520751, 1576432862602739502061

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, A332539.

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

Programs

Mathematica

g[n_] := -(-1)^n*Sum[StirlingS1[n, j]/(j + 1), {j, 1, n}]/n!; Flatten[{3, Numerator[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