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a(n) = 2*n^(2*n)*(1+ sum((1+k^(n+2)/n+k/n)/(n^k*k!), k=1..infinity)) / exp(1/n).
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%I #11 Mar 30 2012 18:39:46

%S 14,89,3104,265832,42711550,11454711984,4840928618302,

%T 3108267243405312,2924919606477510504,3870562086323220000000,

%U 6908112063470228210507358,16038451894952529045493383168,47076979725683125083464370176990,170928617514191160703263296201650176

%N a(n) = 2*n^(2*n)*(1+ sum((1+k^(n+2)/n+k/n)/(n^k*k!), k=1..infinity)) / exp(1/n).

%e n=1: 2*(1+ sum((1+k^3+k)/k!, k=1..infinity))/exp(1) = 14.

%Y Cf. A001113, A092516, A092514, A092041.

%K nonn

%O 1,1

%A _Alexander R. Povolotsky_, Sep 14 2011