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%I M4241
%S 1,1,6,41,365,3984,51499,769159,13031514,246925295,5173842311,
%T 118776068256,2964697094281,79937923931761,2315462770608870,
%U 71705109685449689
%N Number of partitions into pairs.
%C a(n) is the subset of the set of unordered pairings of the first 2n integers (A001147) forbidding pairs of the form (i,i+1) for all i in [2,n-1]. There are many other selections of forbidden pairs giving the same count. [From Olivier Gérard, Feb 8 2011]
%D G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonne, Publications de l'Institut de Statistique de l'Universit\'{e} de Paris, 23 (1978), 57-74.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%F a(n) = |A000806(n-1)|+|A000806(n)|. G.f.: Sum_{n>=0} A001147(n)*(x/(1+x)^2)^n. - _Vladeta Jovovic_, Jun 27 2007
%F Recurrence: (4*n^2-8*n+1)*a(n-1) + (2*n-1)*a(n-2) + (3-2*n)*a(n) = 0. - _Vaclav Kotesovec_, Oct 05 2012
%K nonn
%O 1,3
%A _N. J. A. Sloane_.
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