A356589 - OEIS

A356589

a(n) = n! * Sum_{k=1..n} sigma_k(k)/(k * (n-k)!).

1, 7, 74, 1896, 83829, 6169915, 634444586, 89796130088, 16407420884385, 3792452363345383, 1076168167972120354, 368657061467873013440, 149787334364400115372677, 71262783791831946810277899, 39228224120114488162020163762

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..15.

FORMULA

E.g.f.: -exp(x) * Sum_{k>0} log(1 - (k*x)^k)/k.

a(n) ~ n! * n^(n-1). - Vaclav Kotesovec, Aug 17 2022

MATHEMATICA

a[n_] := n! * Sum[DivisorSigma[k, k]/(k*(n - k)!), {k, 1, n}]; Array[a, 15] (* Amiram Eldar, Aug 14 2022 *)

PROG

(PARI) a(n) = n!*sum(k=1, n, sigma(k, k)/(k*(n-k)!));

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-(k*x)^k)/k)))

CROSSREFS

Cf. A002745, A002746, A356437, A356590.

Sequence in context: A337387 A054745 A323322 * A326221 A197091 A174243

Adjacent sequences: A356586 A356587 A356588 * A356590 A356591 A356592

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 14 2022

STATUS

approved