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%I #11 May 15 2024 01:21:24
%S 1,1,3,9,38,190,1146,8022,64200,577800,5778120,63559320,762712560,
%T 9915263280,138813690960,2082205364400,33315285870720,566359859802240,
%U 10194477476803200,193695072059260800,3873901441188844800,81351930264965740800,1789742465829286214400
%N a(n) = n! * Sum_{k=0..floor(n/2)} k! / (2*k)!.
%F E.g.f.: (1 + sqrt(Pi) * x * exp(x^2/4) * erf(x/2) / 2) / (1 - x).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * k! * (n-2*k)!.
%F a(n) ~ n! * (1 + exp(1/4)*sqrt(Pi)*erf(1/2)/2). - _Vaclav Kotesovec_, May 14 2024
%t Table[n! Sum[k!/(2 k)!, {k, 0, Floor[n/2]}], {n, 0, 22}]
%t nmax = 22; CoefficientList[Series[(1 + Sqrt[Pi] x Exp[x^2/4] Erf[x/2]/2)/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) a(n) = n! * sum(k=0, n\2, k! / (2*k)!); \\ _Michel Marcus_, May 14 2024
%Y Cf. A001813, A009179, A084261.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, May 14 2024
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