A014145 Partial sums of A007489.
0, 1, 4, 13, 46, 199, 1072, 6985, 53218, 462331, 4500244, 48454957, 571411270, 7321388383, 101249656696, 1502852293009, 23827244817322, 401839065437635, 7182224591785948, 135607710526966261, 2696935204638786574, 56349204870460046887, 1234002202313888987200
Offset: 0
Keywords
Examples
a(4) = 1*4! + 2*3! + 3*2! + 4*1! = 46. - _Amarnath Murthy_, Sep 30 2003
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
Programs
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Maple
a:= proc(n) option remember; `if`(n<3, n^2, (n+2)*a(n-1) -(2*n+1)*a(n-2) +n*a(n-3)) end: seq(a(n), n=0..25); # Alois P. Heinz, Jun 16 2017 -
Mathematica
Join[{0},Nest[Accumulate[#]&,Range[20]!,2]] (* Harvey P. Dale, Aug 05 2015 *)
Formula
a(n) = Sum_{k=1..n} k*(n+1-k)!. - Amarnath Murthy, Sep 30 2003
a(n) = A200545(n+1,1). - Philippe Deléham, Nov 19 2011
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
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