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A171777 E.g.f.: A(x) = exp( Sum_{n>=1} 2^(n(n-1)/2) * x^n/n ).

%I A171777 #6 Mar 15 2023 12:35:13
%S A171777 1,1,3,23,473,27057,4102027,1539365191,1365364095921,2783117747148641,
%T A171777 12795599930746180499,130882205973999096722679,
%U A171777 2946911413331842739385098377,144807670567304192694224250060817,15419384323650924141916096692523710747
%N A171777 E.g.f.: A(x) = exp( Sum_{n>=1} 2^(n(n-1)/2) * x^n/n ).
%H A171777 Alois P. Heinz, <a href="/A171777/b171777.txt">Table of n, a(n) for n = 0..77</a>
%e A171777 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 23*x^3/3! + 473*x^4/4! +...
%e A171777 log(A(x)) = x + 2*x^2/2 + 2^3*x^3/3 + 2^6*x^4/4 + 2^10*x^5/5 +...
%p A171777 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
%p A171777       binomial(n-1, j-1)*(j-1)!*2^(j*(j-1)/2), j=1..n))
%p A171777     end:
%p A171777 seq(a(n), n=0..14);  # _Alois P. Heinz_, Mar 15 2023
%o A171777 (PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n+1, 2^(m*(m-1)/2)*x^m/m)+x*O(x^n)), n)}
%Y A171777 Cf. A171776, A155200.
%K A171777 nonn
%O A171777 0,3
%A A171777 _Paul D. Hanna_, Jan 23 2010