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A014145 Partial sums of A007489. 5
0, 1, 4, 13, 46, 199, 1072, 6985, 53218, 462331, 4500244, 48454957, 571411270, 7321388383, 101249656696, 1502852293009, 23827244817322, 401839065437635, 7182224591785948, 135607710526966261, 2696935204638786574, 56349204870460046887, 1234002202313888987200 (list; graph; refs; listen; history; text; internal format)
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 * A143566 A098841 A017944

Adjacent sequences:  A014142 A014143 A014144 * A014146 A014147 A014148

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 21 15:50 EDT 2020. Contains 337272 sequences. (Running on oeis4.)