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%I #52 Jun 06 2018 10:58:16
%S 0,1,2,13,314,37693,27139274,136781978653,5515049406428234,
%T 2001301128741459532573,7262321535982523401207330634,
%U 289888636287509191402441516910783773,138857120603534969958797266489215885728367434
%N a(0) = 0, a(1) = 1, a(n) = n! * a(n-1) + a(n-2).
%C Also numerator of fraction equal to the continued fraction [ 0; 1!, 2!, ... , n! ].
%H Seiichi Manyama, <a href="/A304727/b304727.txt">Table of n, a(n) for n = 0..43</a>
%F a(n) ~ c * BarnesG(n+2), where c = 1.09066686013842761466853962605824103850541289039727399315605573072024... - _Vaclav Kotesovec_, Jun 05 2018
%e a(1) = 1 because [ 0; 1! ] = 1/1.
%e a(2) = 2 because [ 0; 1!, 2! ] = 2/3.
%e a(3) = 13 because [ 0; 1!, 2!, 3! ] = 13/19.
%e a(4) = 314 because [ 0; 1!, 2!, 3!, 4! ] = 314/459.
%Y Cf. A176232.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 05 2018
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