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A086325
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Let u(1)=0, u(2)=1, u(k)=u(k-1)+u(k-2)/(k-2); then a(n)=n!*u(n).
(Formerly N0672)
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1
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0, 2, 6, 36, 220, 1590, 12978, 118664, 1201464, 13349610, 161530270, 2114578092, 29780308116, 448995414686, 7215997736010, 123153028027920, 2224451568754288, 42395429898611154, 850263899633257014, 17900292623858042420, 394701452356069835340, 9096928711444657157382, 218739785834282892557026
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OFFSET
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1,2
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263, Table 7.5.1, row 3.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210, Table 3, Three-line Latin rectangles.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..23.
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FORMULA
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a(n) = ceiling(n*n!/e) - (1-(-1)^n)/2.
E.g.f.: x^2*exp(-x)/(1-x)^2. - Vladeta Jovovic, Nov 20 2003
a(n) = n*floor((n!+1)/e) [From Gary Detlefs, Jul 13 2010]
a(n) = n * A000166(n). [Joerg Arndt, Jul 09 2012]
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MAPLE
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a:=n->n!*add((-1)^k/k!, k=0..n): seq(a(n)*n, n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 18 2007
with (combstruct):with (combinat):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(2):seq(count(ZLL, size=n)*fibonacci(2, n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
with (combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(2):seq(count(ZLL, size=n)*n, n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
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MATHEMATICA
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Table[Subfactorial[n]*n, {n, 1, 19}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2009]
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CROSSREFS
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Cf. A000246, A000274, A000166.
Sequence in context: A101609 A152668 A213918 * A074424 A002868 A002869
Adjacent sequences: A086322 A086323 A086324 * A086326 A086327 A086328
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KEYWORD
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nonn,changed
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AUTHOR
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N. J. A. Sloane. This sequence appeared in the 1973 "Handbook", but was then omitted from the database. Resubmitted by Benoit Cloitre, Aug 30 2003. Entry revised by N. J. A. Sloane, Jun 11 2012
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STATUS
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approved
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