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A014145 Partial sums of A007489.

%I A014145 #36 Mar 30 2018 03:21:30
%S A014145 0,1,4,13,46,199,1072,6985,53218,462331,4500244,48454957,571411270,
%T A014145 7321388383,101249656696,1502852293009,23827244817322,401839065437635,
%U A014145 7182224591785948,135607710526966261,2696935204638786574,56349204870460046887,1234002202313888987200
%N A014145 Partial sums of A007489.
%H A014145 Vincenzo Librandi, <a href="/A014145/b014145.txt">Table of n, a(n) for n = 0..200</a>
%H A014145 Alexsandar Petojevic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Petojevic/petojevic5.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
%F A014145 a(n) = Sum_{k=1..n} k*(n+1-k)!. - _Amarnath Murthy_, Sep 30 2003
%F A014145 a(n) = A200545(n+1,1). - _Philippe Deléham_, Nov 19 2011
%F A014145 a(n) = (n+2)*a(n-1) -(2*n+1)*a(n-2) +n*a(n-3) for n > 2, a(n) = n^2 for n < 3. - _Alois P. Heinz_, Jun 16 2017
%F A014145 a(n) ~ n! * (1 + 2/n + 3/n^2 + 7/n^3 + 20/n^4 + 67/n^5 + 255/n^6 + 1080/n^7 + 5017/n^8 + 25287/n^9 + 137122/n^10 + ...), for coefficients see A011968. - _Vaclav Kotesovec_, Mar 30 2018
%e A014145 a(4) = 1*4! + 2*3! + 3*2! + 4*1! = 46. - _Amarnath Murthy_, Sep 30 2003
%p A014145 a:= proc(n) option remember; `if`(n<3, n^2,
%p A014145       (n+2)*a(n-1) -(2*n+1)*a(n-2) +n*a(n-3))
%p A014145     end:
%p A014145 seq(a(n), n=0..25);  # _Alois P. Heinz_, Jun 16 2017
%t A014145 Join[{0},Nest[Accumulate[#]&,Range[20]!,2]] (* _Harvey P. Dale_, Aug 05 2015 *)
%K A014145 nonn
%O A014145 0,3
%A A014145 _N. J. A. Sloane_