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A014144 Apply partial sum operator twice to factorials. 4
0, 1, 3, 7, 17, 51, 205, 1079, 6993, 53227, 462341, 4500255, 48454969, 571411283, 7321388397, 101249656711, 1502852293025, 23827244817339, 401839065437653, 7182224591785967, 135607710526966281 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equals row sums of triangle A137948 starting with offset 1. - Gary W. Adamson, Feb 28 2008

If s(n) is a sequence defined as s(0)=a, s(1)=b, s(n) = n*(s(n-1) - s(n-2)), n>1, then s(n) = n*b - (a(n)-1)*a. - Gary Detlefs, Feb 23 2011

LINKS

Table of n, a(n) for n=0..20.

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

Index entries for sequences related to factorial numbers

FORMULA

a(n) = (n-1) * !n - n! + 1, !n = sum[ k=0..n-1 ] k!. - Joe Keane (jgk(AT)jgk.org)

a(n) = convolution(A000142, A001477). - Peter Luschny, Jan 21 2012

G.f.: x*G(0)/(1-x)^2, where G(k)= 1 + (2*k + 1)*x/( 1 - 2*x*(k+1)/(2*x*(k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 24 2013

MATHEMATICA

Accumulate@ Accumulate@ (Range[0, 19]!) (* Robert G. Wilson v *)

lst={}; s0=s1=0; Do[s0+=a[n]; s1+=s0; AppendTo[lst, s1], {n, 0, 2*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 10 2008 *)

PROG

(PARI) a(n)=(n-1)*round(n!/exp(1))-n!+1 \\ Charles R Greathouse IV, Feb 24 2011

CROSSREFS

Cf. A000142, A003422, A137948.

Sequence in context: A071985 A181419 A090977 * A247183 A096358 A260349

Adjacent sequences:  A014141 A014142 A014143 * A014145 A014146 A014147

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 22 09:44 EDT 2017. Contains 292337 sequences.