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%I #12 Oct 29 2017 04:10:55
%S 1,1,2,8,60,732,12672,283704,7757526,249885110,9255184676,
%T 387336669496,18075315527932,930651571119228,52411013929403760,
%U 3205007479811374344,211500660045169230729,14981245823696876792553,1133747667225683826679642,91294225766212875597830080,7793993663152146113116892960,703185550242112366418746032320,66853101136423829966807930994240
%N G.f.: exp( Sum_{n>=1} A294330(n) * x^n / n ).
%H Paul D. Hanna, <a href="/A294331/b294331.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) ~ c * d^n * n^(n-2), where d = 1.788680223969315995... and c = 0.254472375755339325... - _Vaclav Kotesovec_, Oct 29 2017
%e G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 60*x^4 + 732*x^5 + 12672*x^6 + 283704*x^7 + 7757526*x^8 + 249885110*x^9 + 9255184676*x^10 +...
%e such that
%e log(A(x)) = x + 3*x^2/2 + 19*x^3/3 + 207*x^4/4 + 3331*x^5/5 + 71223*x^6/6 + 1890379*x^7/7 + 59652687*x^8/8 + 2175761971*x^9/9 +...+ A294330(n)*x^n/n +...
%e where the e.g.f. G(x) of A294330 begins
%e G(x) = x + 3*x^2/2! + 19*x^3/3! + 207*x^4/4! + 3331*x^5/5! + 71223*x^6/6! + 1890379*x^7/7! +...+ A294330(n)*x^n/n! +...
%e and satisfies: Product_{n>=1} (1 - (-G(x))^n) = exp(x).
%o (PARI) {A294330(n) = my( L = sum(m=1, n, (-1)^(m-1) * sigma(m) * x^m/m ) +x*O(x^n) ); n!*polcoeff( serreverse(L), n)}
%o {a(n) = my(A); A = exp( sum(m=1,n+1, A294330(m)*x^m/m +x*O(x^n)) ); polcoeff(A,n)}
%o for(n=0, 25, print1(a(n), ", "))
%Y Cf. A294330.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 28 2017
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