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%I #21 Nov 06 2020 03:53:22
%S 5,6,14,48,216,1200,7920,60480,524160,5080320,54432000,638668800,
%T 8143027200,112086374400,1656387532800,26153487360000,439378587648000,
%U 7825123418112000,147254595231744000,2919482409811968000,60822550204416000000,1328364496464445440000
%N a(n) = n*a(n-1) + n!, with n>0, a(0)=5.
%D C. Mariconda and A. Tonolo, Calcolo discreto, Apogeo (2012), page 240 (Example 9.57 gives the recurrence).
%F E.g.f.: (5 - 4*x)/(1 - x)^2.
%F a(n) = (n + 5)*n!.
%F a(n) = 2*A229039(n) for n>0.
%F From _Amiram Eldar_, Nov 06 2020: (Start)
%F Sum_{n>=0} 1/a(n) = 9*e - 24.
%F Sum_{n>=0} (-1)^n/a(n) = 24 - 65/e. (End)
%t RecurrenceTable[{a[0] == 5, a[n] == n a[n - 1] + n!}, a, {n, 0, 30}] (* or *)
%t Table[(n + 5) n!, {n, 0, 30}]
%Y Cf. A229039.
%Y Cf. sequences with formula (n + k)*n!: A052521 (k=-5), A282822 (k=-4), A052520 (k=-3), A052571 (k=-2), A062119 (k=-1), A001563 (k=0), A000142 (k=1), A001048 (k=2), A052572 (k=3), A052644 (k=4), this sequence (k=5).
%K nonn,easy
%O 0,1
%A _Bruno Berselli_, Feb 22 2017
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