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A123023
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a(n) = b(n)*n!, where b(n+2)=n*b(n)/((n+2)*(n+1)), b(0)=0, b(1)=1.
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1
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1, 1, 0, 1, 0, 3, 0, 15, 0, 105, 0, 945, 0, 10395, 0, 135135, 0, 2027025, 0, 34459425, 0, 654729075, 0, 13749310575, 0, 316234143225, 0, 7905853580625, 0, 213458046676875, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| a(n) is the number of ways of separating n terms into pairs - Stephen Crowley (crow(AT)crowlogic.net), Apr 07 2007
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REFERENCES
| Richard Bronson, Schaum's Outline of Modern Introductory Differential Equations, MacGraw-Hill, New York,1973, page 107, solved problem 19.18
Norbert Wiener, Nonlinear Problems in Random Theory, 1958, Equation 1.31
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FORMULA
| a(n)=(1/2)*GAMMA((1/2)*n+1/2)*2^((1/2)*n)*(1+(-1)^n)/sqrt(Pi) - Stephen Crowley (crow(AT)crowlogic.net), Apr 07 2007
With offset -1, E.g.f.:exp(x^2/2) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 15 2009]
a(2n) = A001147(n-1). - R. J. Mathar, Oct 11 2011
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MAPLE
| with(combstruct):ZL2:=[S, {S=Set(Cycle(Z, card=2))}, labeled]:seq(count(ZL2, size=n), n=1..28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 24 2007
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MATHEMATICA
| a[n_] := a[n] = (n - 2)*a[n - 2]/(n*(n - 1)); a[0] = 1; a[1] = 1; Table[a[n]*n!, {n, 0, 30}]
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CROSSREFS
| Sequence in context: A065121 A167339 A138540 * A130637 A054882 A086479
Adjacent sequences: A123020 A123021 A123022 * A123024 A123025 A123026
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KEYWORD
| nonn
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 24 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 06 2008
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