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

0,1

Links

Table of n, a(n) for n=0..22.

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[{3, Numerator[Table[Sum[g[k]*g[n + 1 - k], {k, 1, n}]/n, {n, 1, 30}]]}] (* Vaclav Kotesovec, Feb 16 2020 *)

Crossrefs

Cf. A002206, A002207, A332539.

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

Sequence in context: A010273 A046143 A228035 * A071812 A248133 A177992

Adjacent sequences: A332535 A332536 A332537 * A332539 A332540 A332541

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2020

Extensions

More terms from Vaclav Kotesovec, Feb 16 2020

Status

approved