A360091 Numerator of (n-2)!*Sum_{k=1..n} (-1)^(k+1)/((n-k)!*k^k).

3, 31, 517, 322537, 2840123, 324200318207, 1285595921612117, 73566451396634047493, 44670351166870486810889, 1129160781485410557635298647751929, 1103929347366548607910442339939699, 25219262227183500148649140605496240723288052699

Offset

2,1

Links

Amiram Eldar, Table of n, a(n) for n = 2..57

David Peter Hadrian Ulgenes, Series and Product Representations of Gamma and Pseudogamma Functions, arXiv:2301.09699 [math.NT], 2023.

Formula

-1 + Sum_{n>=2} a(n)/A360092(n) = gamma (A001620) (Ulgenes, 2023, Corollary 2). - Amiram Eldar, Jan 25 2023

Mathematica

Array[Numerator[(# - 2)!*Sum[(-1)^(k + 1)/((# - k)!*k^k), {k, #}]] &, 13, 2] (* Michael De Vlieger, Jan 25 2023 *)

Prog

(PARI) a(n) = numerator((n-2)!*sum(k=1, n, (-1)^(k+1)/((n-k)!*k^k)));

Crossrefs

Cf. A001620, A360092 (denominators).

Sequence in context: A346313 A143637 A327227 * A245109 A121563 A360343

Adjacent sequences: A360088 A360089 A360090 * A360092 A360093 A360094

Keyword

nonn,frac

Author

Michel Marcus, Jan 25 2023

Status

approved