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A007489
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Sum of k!, k=1..n.
(Formerly M2818)
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33
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0, 1, 3, 9, 33, 153, 873, 5913, 46233, 409113, 4037913, 43954713, 522956313, 6749977113, 93928268313, 1401602636313, 22324392524313, 378011820620313, 6780385526348313, 128425485935180313, 2561327494111820313, 53652269665821260313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Equals row sums of triangle A143122 starting (1, 3, 9, 33,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 26 2008
A007489(n) for n>=4 does not yield a perfect square [From Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 16 2008]
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 14 2009: (Start)
Number of cycles that can be written in the form (j,j+1,j+2,...), in all permutations of {1,2,...,n}. Example: a(3)=9 because in (1)(2)(3), (1)(23), (12)(3), (13)(2), (123), (132) we have 3+2+2+1+1+0=9 such cycles.
(End)
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
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
Eric Weisstein's World of Mathematics, Factorial
G. Xiao, Sigma Server, Operate on "n!"
Index entries for sequences related to factorial numbers
Eric Weisstein's World of Mathematics, Left Factorial
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FORMULA
| a(n) = Sum[P(n, k) / C(n, k) {k=1...n}] - Ross La Haye (rlahaye(AT)new.rr.com), Sep 21 2004
a(n)=3*A056199(n) for n>=2 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 10 2007
a(n)=!(n+1)+1=A003422(n+1)+1 - Artur Jasinski, Nov 08 2007
Starting (1, 3, 9, 33, 153,...), = row sums of triangle A137593 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 28 2008
a(n) = a(n-1) + n! for n >= 2. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jun 16 2009]
E.g.f. A(x) satisfies to the differential equation A'(x)=A(x)+x/(1-x)^2+1. [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Jan 22 2011]
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MAPLE
| A007489 := proc(n) local i; add(i!, i=1..n); end;
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MATHEMATICA
| FoldList[Plus, 0, (Range@ 21)! ] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 21 2007 *)
Table[Sum[i!, {i, 1, n}], {n, 0, 21}] (* From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009 *)
Accumulate[Range[50]!] (* From Harvey P. Dale, Apr 30 2011 *)
Table[Plus@@(Range[n]!), {n, 20}] (* From Alonso del Arte, Jul 18 2011 *)
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PROG
| (PARI) a(n)=sum(k=1, n, k!) \\ Charles R Greathouse IV, Jul 25 2011
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CROSSREFS
| Equals A003422(n+1) - 1.
Cf. A137593.
Cf. A143122.
A161128 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 14 2009]
Sequence in context: A012584 A101899 A009220 * A201968 A097677 A138769
Adjacent sequences: A007486 A007487 A007488 * A007490 A007491 A007492
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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