A054201 a(n) = (n-1)! * Sum_{k=1..n} k^k/k!.

1, 3, 15, 109, 1061, 13081, 196135, 3470097, 70807497, 1637267473, 42310099331, 1208419463329, 37799118682429, 1285103316125721, 47184372451150719, 1860687091374107761, 78432185337652592657, 3519258710478790607137, 167474007086529472461307

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..385

Formula

-LambertW(-x)/(1+LambertW(-x))/(1-x) = Sum_{n>=1} a(n)*x^n/(n-1)!. - Vladeta Jovovic, Aug 26 2002

a(n) ~ exp(1)/(exp(1)-1) * n^(n-1). - Vaclav Kotesovec, Oct 18 2013

a(n) = (n-1)!*Sum_{i=1..n} Product_{j=1..i} i/j. - Pedro Caceres, Apr 19 2019

Example

a(3) = 2! *(1^1/1! + 2^2/2! + 3^3/3!) = 2 *(1/1 + 4/2 + 27/6) = 15.

Mathematica

Table[(n-1)!*Sum[k^k/k!, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 18 2013 *)

Prog

(PARI) vector(20, n, (n-1)!*sum(k=1, n, k^k/k!)) \\ G. C. Greubel, Jul 31 2019
(Magma) F:=Factorial; [F(n-1)*(&+[k^k/F(k): k in [1..n]]): n in [1..20]]; // G. C. Greubel, Jul 31 2019
(Sage) f=factorial; [f(n-1)*sum(k^k/f(k) for k in (1..n)) for n in (1..20)] # G. C. Greubel, Jul 31 2019
(GAP) F:=Factorial;; List([1..20], n-> F(n-1)*Sum([1..n], k-> k^k/F(k))); # G. C. Greubel, Jul 31 2019

Crossrefs

Cf. A054202.

Sequence in context: A153305 A110328 A217061 * A090355 A083483 A089468

Adjacent sequences: A054198 A054199 A054200 * A054202 A054203 A054204

Keyword

nonn,easy

Author

Leroy Quet, Apr 29 2000

Status

approved