A332540 Numerators of coefficients in a series for Euler's constant gamma (negated).

3, 1, 1, 29, 67, 1507, 3121, 12703, 164551, 6344953, 147727471, 27529188163, 710710333, 271695249739, 1866529128749, 21255957303929, 908965802898697, 12844144201070519, 228917805573310159, 185233029315627847397, 104416844507809792139, 45256363943072384591371

Offset

0,1

Links

Table of n, a(n) for n=0..21.

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. 2 to Th. 2.

Xavier Gourdon and Pascal Sebah, Collection of formulae for Euler's constant gamma.

Formula

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

gamma = 2*log(2*Pi) - Sum_{k>=0} A332540(k)/A332541(k). - Hugo Pfoertner, Feb 16 2020

Mathematica

g[n_] := -(-1)^n*Sum[StirlingS1[n, j]/(j + 1), {j, 1, n}]/n!; Flatten[{3, Table[Numerator[2*Sum[g[k]*g[n + 2 - k], {k, 1, n}]/(n + 1)], {n, 1, 25}]}] (* Vaclav Kotesovec, Feb 16 2020 *)

Crossrefs

Cf. A002206, A002207, A332541.

Cf. A001620 (Euler's constant gamma).

Sequence in context: A216922 A245243 A168242 * A215750 A126465 A077509

Adjacent sequences: A332537 A332538 A332539 * A332541 A332542 A332543

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2020

Extensions

More terms from Vaclav Kotesovec, Feb 16 2020

Status

approved