A165792 a(0)=1, a(n) = n*(a(n-1)+2).

1, 3, 10, 36, 152, 770, 4632, 32438, 259520, 2335698, 23357000, 256927022, 3083124288, 40080615770, 561128620808, 8416929312150, 134670868994432, 2289404772905378, 41209285912296840, 782976432333639998, 15659528646672800000, 328850101580128800042

Offset: 0

Author

Philippe Deléham, Sep 26 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A000142, A033540.

Programs

Mathematica

FoldList[#1*#2 + 2 #2 &, 1, Range[19]](* Robert G. Wilson v, Jul 07 2012 *)
NestList[{#[[1]]+1,(#[[1]]+1)(#[[2]]+2)}&,{0,1},20][[All,2]] (* Harvey P. Dale, Jul 03 2021 *)

Formula

a(n) = n! + 2*floor(e*n!)-2, n>0. - Gary Detlefs, Jun 06 2010

E.g.f.: (1 + 2 * x * exp(x)) / (1 - x). - Ilya Gutkovskiy, Oct 11 2021

Extensions

Definition corrected by Philippe Deléham, Sep 28 2009