%I A123023
%S A123023 1,1,0,1,0,3,0,15,0,105,0,945,0,10395,0,135135,0,2027025,0,34459425,0,
%T A123023 654729075,0,13749310575,0,316234143225,0,7905853580625,0,
%U A123023 213458046676875,0
%N A123023 a(n) = b(n)*n!, where b(n+2)=n*b(n)/((n+2)*(n+1)), b(0)=0, b(1)=1.
%C A123023 a(n) is the number of ways of separating n terms into pairs - Stephen 
               Crowley (crow(AT)crowlogic.net), Apr 07 2007
%D A123023 Richard Bronson, Schaum's Outline of Modern Introductory Differential 
               Equations, MacGraw-Hill, New York,1973, page 107, solved problem 
               19.18
%D A123023 Norbert Wiener, Nonlinear Problems in Random Theory, 1958, Equation 1.31
%F A123023 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
%F A123023 With offset -1, E.g.f.:exp(x^2/2) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Mar 15 2009]
%p A123023 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
%t A123023 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}]
%Y A123023 Sequence in context: A065121 A167339 A138540 this_sequence A130637 A054882 
               A086479
%Y A123023 Adjacent sequences: A123020 A123021 A123022 this_sequence A123024 A123025 
               A123026
%K A123023 nonn
%O A123023 1,6
%A A123023 Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 24 2006
%E A123023 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 06 2008