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%I #14 Jun 18 2022 14:00:04
%S 1,1,4,55,2539,383860,187659181,293630900689,1459799672901004,
%T 22924423319469919651,1131844225175191511724871,
%U 175015470856131731421651730600,84480805958219938739735661779357401,126948830401157131161305967764668449231937
%N G.f.: Sum_{n>=0} a(n)*x^n/(n!*3^(n*(n-1)/2)) = exp( Sum_{n>=1} x^n/(n!*3^(n*(n-1)/2)) ).
%o (PARI) a(n) = n!*3^(n*(n-1)/2)*polcoef(exp(sum(k=1, n, x^k/(k!*3^(k*(k-1)/2)))+x*O(x^n)), n);
%o (PARI) T(n, k) = if(k==1, 1, sum(j=1, n-1, 3^(j*(n-j))*binomial(n-1, j)*T(j, k-1)));
%o a(n) = if(n==0, 1, sum(k=1, n, T(n, k)));
%Y Cf. A000110, A240936, A355074.
%Y Cf. A355070, A355081.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 18 2022
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