A053817 a(0)=1, a(n) = n*(a(n-1) + n).

1, 2, 8, 33, 148, 765, 4626, 32431, 259512, 2335689, 23356990, 256927011, 3083124276, 40080615757, 561128620794, 8416929312135, 134670868994416, 2289404772905361, 41209285912296822, 782976432333639979, 15659528646672799980, 328850101580128800021

Offset: 0

Author

mindy and steve schwartz (minsteve(AT)netvision.net.il), Apr 07 2000

Keywords

• nonn
• easy
• nice

Examples

			Start with 1, add 1, multiply by 1 (getting 2), add 2, multiply by 2 (getting 8).
		

Crossrefs

Cf. A019460, A030297.

Programs

Maple

a:= proc(n) a(n):= n*(a(n-1) + n) end: a(0):= 1:
seq(a(n), n=0..23);  # Alois P. Heinz, May 12 2021

Mathematica

a=1;lst={a};Do[a=(a+n)*n;AppendTo[lst, a], {n, 2*4!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2008 *)
RecurrenceTable[{a[0]==1,a[n]==n(a[n-1]+n)},a,{n,20}] (* Harvey P. Dale, Feb 14 2015 *)

Formula

a(n) = A030297(n) + n! = A019460(2n+1) - n. - Henry Bottomley, Nov 10 2000

a(n)= n! + floor(2*e*n!-n) - 2, n>1. - Gary Detlefs, Jun 22 2010

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

Extensions

More terms from James Sellers, Apr 08 2000