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%I #23 Oct 11 2021 09:46:09
%S 1,2,8,33,148,765,4626,32431,259512,2335689,23356990,256927011,
%T 3083124276,40080615757,561128620794,8416929312135,134670868994416,
%U 2289404772905361,41209285912296822,782976432333639979,15659528646672799980,328850101580128800021
%N a(0)=1, a(n) = n*(a(n-1) + n).
%F a(n) = A030297(n) + n! = A019460(2n+1) - n. - _Henry Bottomley_, Nov 10 2000
%F a(n)= n! + floor(2*e*n!-n) - 2, n>1. - _Gary Detlefs_, Jun 22 2010
%F E.g.f.: (1 + x * (1 + x) * exp(x)) / (1 - x). - _Ilya Gutkovskiy_, Oct 11 2021
%e Start with 1, add 1, multiply by 1 (getting 2), add 2, multiply by 2 (getting 8).
%p a:= proc(n) a(n):= n*(a(n-1) + n) end: a(0):= 1:
%p seq(a(n), n=0..23); # _Alois P. Heinz_, May 12 2021
%t a=1;lst={a};Do[a=(a+n)*n;AppendTo[lst, a], {n, 2*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2008 *)
%t RecurrenceTable[{a[0]==1,a[n]==n(a[n-1]+n)},a,{n,20}] (* _Harvey P. Dale_, Feb 14 2015 *)
%Y Cf. A019460, A030297.
%K nonn,easy,nice
%O 0,2
%A mindy and steve schwartz (minsteve(AT)netvision.net.il), Apr 07 2000
%E More terms from _James A. Sellers_, Apr 08 2000
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