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A000774
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n!*(1+ Sum(i=1..n, 1/i )).
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9
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1, 2, 5, 17, 74, 394, 2484, 18108, 149904, 1389456, 14257440, 160460640, 1965444480, 26029779840, 370643938560, 5646837369600, 91657072281600, 1579093018675200, 28779361764249600, 553210247226470400, 11185850044938240000, 237335752951879680000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of {12,12*,21}-avoiding signed permutations in the hyperoctahedral group.
Let M be the n X n matrix with M( i, i ) = i+1, other entries = 1. Then a(n) = det(M); example : a(3) = 17 = det([2, 1, 1; 1, 3, 1; 1, 1, 4]) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 13 2005.
With offset 1: number of permutations of the n-set into at most two cycles. [From Joerg Arndt, Jun 22 2009]
Contribution from Weisenhorn Paul, Jun 03 2010: (Start)
A ball goes with probability 1/(k+1) from place k to a place j with j=0..k
a(n)/n! is the average number of steps from place n to place 0
(End)
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REFERENCES
| J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups. Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..250
C. Lenormand, Arbres et permutations II, see p. 9
T. Mansour and J. West, Avoiding 2-letter signed patterns.
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FORMULA
| E.g.f.: A(x) = (1-x)^-1 * (1 - log(1-x))
a(n+1)=(n+1)*a(n) + n! - Jon Perry, Sep 26 2004
A000774(n) = A000254(n) + n! [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 06 2010]
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EXAMPLE
| (1-x)^-1 * (1 - log(1-x)) = 1 + 2*x + 5/2*x^2 + 17/6*x^3 + ...
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MAPLE
| A000774 := proc(n) local i, j; j := 0; for i to n do j := j+1/i od; (j+1)*n! end;
ZL :=[S, {S = Set(Cycle(Z), 3 > card)}, labelled]: seq(combstruct[count](ZL, size=n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008
Contribution from Weisenhorn Paul, Jun 03 2010: (Start)
a[0]:=1: p:=1: for n from 1 to 20 do
a[n]:=n*a[n-1]+p: p:=p*n: end do:
(End)
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MATHEMATICA
| Table[n!(1+Sum[1/i, {i, n}]), {n, 0, 30}] (* From Harvey P. Dale, Oct 03 2011 *)
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PROG
| (PARI) a(n)=n!*(1+sum(j=1, n, 1/j ));
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CROSSREFS
| Cf. A000254, A000776. Same as A081046 apart from signs.
Sequence in context: A136726 A112831 A081046 * A118100 A129591 A099825
Adjacent sequences: A000771 A000772 A000773 * A000775 A000776 A000777
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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