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%I M4263 #21 Sep 25 2018 21:12:01
%S 1,6,55,610,7980,120274,2052309,39110490,823324755,18974858540,
%T 475182478056,12848667150956,373081590628565,11578264139795430,
%U 382452947343624515,13397354334102974934,496082324933446766724,19360538560004548357830,794275868644522931369185
%N Number of partitions into pairs.
%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'Université 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) = A079267(n + 2, 3). - _Sean A. Irvine_, Jan 24 2017
%F a(n) ~ 2^(n + 3/2) * n^(n + 2) / (3 * exp(n + 1)). - _Vaclav Kotesovec_, May 20 2018
%p a:= proc(n) option remember; `if`(n<2, n,
%p (n*(4*n^2-7)*a(n-1)+(n+1)*(2*n+1)*a(n-2))/((2*n-1)*(n-1)))
%p end:
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Jan 24 2017
%t Table[(2*n+1)! * Hypergeometric1F1[1-n, -1-2*n, -2] / (3*2^n*(n-1)!), {n, 1, 20}] (* _Vaclav Kotesovec_, Jan 24 2017 *)
%Y Cf. A079267.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Jan 24 2017