%I #22 Mar 03 2024 16:49:40

%S 1,1,1,4,13,46,241,1156,6889,44668,300241,2328976,18390901,159273544,

%T 1461200833,13995753136,144068872081,1531949061136,17259159775969,

%U 202543867724608,2474236899786781,31633380519660256,417760492214548561,5751414293905728064

%N Expansion of e.g.f. exp( x * exp(x^2/2) ).

%H Seiichi Manyama, <a href="/A354550/b354550.txt">Table of n, a(n) for n = 0..518</a>

%F a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * k! * (n - 2*k)!).

%t With[{nn=30},CoefficientList[Series[Exp[x Exp[x^2/2]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 03 2024 *)

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)))))

%o (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!*(n-2*k)!));

%Y Cf. A000248, A354551, A354552.

%Y Cf. A216688.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Aug 18 2022