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G.f.: Sum_{n>=0} a(n)*x^n/(n!*4^(n*(n-1)/2)) = exp( Sum_{n>=1} x^n/(n!*4^(n*(n-1)/2)) ).
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%I #13 Jun 18 2022 14:00:13

%S 1,1,5,113,11265,4859137,8966576129,70171067707393,

%T 2313986342570295297,319893682564775147012097,

%U 184627527352223449064321581057,443344010564094761887045848673550337,4416539344305075410912848824562640662560769

%N G.f.: Sum_{n>=0} a(n)*x^n/(n!*4^(n*(n-1)/2)) = exp( Sum_{n>=1} x^n/(n!*4^(n*(n-1)/2)) ).

%o (PARI) a(n) = n!*4^(n*(n-1)/2)*polcoef(exp(sum(k=1, n, x^k/(k!*4^(k*(k-1)/2)))+x*O(x^n)), n);

%o (PARI) T(n, k) = if(k==1, 1, sum(j=1, n-1, 4^(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, A355073.

%Y Cf. A355071, A355082.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 18 2022