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

0,3

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

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

Example

a(4) = 1*4! + 2*3! + 3*2! + 4*1! = 46. - Amarnath Murthy, Sep 30 2003

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 *)

Crossrefs

Sequence in context: A151448 A218667 A149439 * A354550 A143566 A098841

Adjacent sequences: A014142 A014143 A014144 * A014146 A014147 A014148

Keyword

nonn

Author

N. J. A. Sloane

Status

approved