A332536 Numerators of coefficients in a series for the first Stieltjes constant gamma_1.

1, 5, 1313, 42169, 137969, 1128119, 8357708899, 4784812183, 6426498401023, 1290156663524207, 2967978587600828623, 40788897698984251631, 4438036185262071403841, 483740902966638267491, 13885929879719429182837579, 646524082127557655708798341

Offset

2,2

Links

Table of n, a(n) for n=2..17.

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!; 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}] // Numerator (* Vaclav Kotesovec, Feb 16 2020 *)

Crossrefs

Cf. A002206, A002207, A332537.

Sequence in context: A268485 A066162 A096725 * A172920 A062598 A203690

Adjacent sequences: A332533 A332534 A332535 * A332537 A332538 A332539

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2020

Extensions

More terms from Vaclav Kotesovec, Feb 16 2020

Status

approved