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%I #17 Mar 17 2018 17:46:06
%S 1,-1,-1,-9,-134,-2852,-79096,-2699480,-109201844,-5100872244,
%T -269903909820,-15944040740604,-1039553309158964,-74123498185170292,
%U -5736368141560365292,-478780244956262592748,-42865943103053965559668,-4097785410628237071311764,-416572537937169684523985420,-44873737158384968851319470220,-5106038963454360810619516396820,-611986780692307637617151164361140,-77066319756799442735378541663266476
%N O.g.f. A(x) satisfies: [x^n] exp( n^2 * A(x) ) = [x^(n-1)] exp( n^2 * A(x) ) for n>=1.
%C E.g.f. G(x) of A296170 satisfies: [x^(n-1)] G(x)^(n^2) = [x^n] G(x)^(n^2) for n>=1.
%H Paul D. Hanna, <a href="/A296171/b296171.txt">Table of n, a(n) for n = 1..300</a>
%e G.f. A(x) = x - x^2 - x^3 - 9*x^4 - 134*x^5 - 2852*x^6 - 79096*x^7 - 2699480*x^8 - 109201844*x^9 - 5100872244*x^10 - 269903909820*x^11 - 15944040740604*x^12 - 1039553309158964*x^13 - 74123498185170292*x^14 - 5736368141560365292*x^15 + ...
%e such that
%e G(x) = exp(A(x)) = 1 + x - x^2/2! - 11*x^3/3! - 239*x^4/4! - 17059*x^5/5! - 2145689*x^6/6! - 412595231*x^7/7! - 111962826751*x^8/8! - 40590007936199*x^9/9! - 18900753214178609*x^10/10! + ... + A296170(n)*x^n/n! + ...
%e satisfies [x^(n-1)] G(x)^(n^2) = [x^n] G(x)^(n^2) for n>=1.
%e RELATED SERIES.
%e Series_Reversion(A(x)) = x + x^2 + 3*x^3 + 19*x^4 + 226*x^5 + 4259*x^6 + 110514*x^7 + 3626207*x^8 + 143043592*x^9 + 6567931068*x^10 + 343278693103*x^11 + 20092744961109*x^12 + 1300754163383700*x^13 + ... + A295812(n)*x^n + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n+1, A=concat(A,0); V=Vec(Ser(A)^((#A-1)^2)); A[#A] = (V[#A-1] - V[#A])/(#A-1)^2 ); polcoeff(log(Ser(A)),n)}
%o for(n=1,30,print1(a(n),", "))
%Y Cf. A296170, A295812, A296173, A296175, A296177.
%K sign
%O 1,4
%A _Paul D. Hanna_, Dec 07 2017
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