A332541 Denominators of coefficients in a series for Euler's constant gamma.

1, 24, 54, 2880, 10800, 362880, 1058400, 5806080, 97977600, 4790016000, 138311712000, 31384184832000, 971415244800, 439378587648000, 3530720793600000, 46562717859840000, 2285647412944896000, 36785478363630796800, 741528257908838400000, 674400436666564608000000

Offset

0,2

Comments

Conjecture: For n > 0, a(n) is a Zumkeller number (A083207). Verified form all n in [2,19]. - Ivan N. Ianakiev, Feb 17 2020

Links

Table of n, a(n) for n=0..19.

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. (a(7) is wrong in the printed version.)

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[{1, Table[Denominator[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, A332540.

Cf. also A001620 (Euler's constant gamma).

Sequence in context: A003756 A135191 A216697 * A316361 A277108 A039375

Adjacent sequences: A332538 A332539 A332540 * A332542 A332543 A332544

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2020

Extensions

a(7) corrected by and more terms from Vaclav Kotesovec, Feb 16 2020

Status

approved