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%I #7 Dec 07 2017 01:56:30
%S 1,-15,-6090,-30600650,-593306350650,-31192838317208826,
%T -3652177141294409632400,-836986399841753367052602000,
%U -342157863774785896821739864893375,-232492750600387706453977026534258393375,-248374508240426643818180115122847840121356750,-398845502818641863837604075681689663598753652620750
%N G.f. equals the logarithm of the e.g.f. of A296176.
%C E.g.f. G(x) of A296176 satisfies: [x^(n-1)] G(x)^(n^5) = [x^n] G(x)^(n^5) for n>=1.
%H Paul D. Hanna, <a href="/A296177/b296177.txt">Table of n, a(n) for n = 1..150</a>
%e G.f. A(x) = x - 15*x^2 - 6090*x^3 - 30600650*x^4 - 593306350650*x^5 - 31192838317208826*x^6 - 3652177141294409632400*x^7 - 836986399841753367052602000*x^8 - 342157863774785896821739864893375*x^9 - 232492750600387706453977026534258393375*x^10 +...
%e such that
%e G(x) = exp(A(x)) = 1 + x - 29*x^2/2! - 36629*x^3/3! - 734559239*x^4/4! - 71200423546199*x^5/5! - 22459270436075644469*x^6/6! - 18407129959728493123679069*x^7/7! - 33747438879000326056232288023439*x^8/8! - 124162549312926509293620790889452447919*x^9/9! - 843670934957017748849439817665935283173590349*x^10/10! +...
%e satisfies [x^(n-1)] G(x)^(n^5) = [x^n] G(x)^(n^5) for n>=1.
%e Series_Reversion(A(x)) = x + 15*x^2 + 6540*x^3 + 31074275*x^4 + 596201157450*x^5 + 31256650109242326*x^6 + 3655957957134009767520*x^7 + 837481638576442353884460435*x^8 +...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n+1, A=concat(A,0); V=Vec(Ser(A)^((#A-1)^5)); A[#A] = (V[#A-1] - V[#A])/(#A-1)^5 ); polcoeff(log(Ser(A)),n)}
%o for(n=1,30,print1(a(n),", "))
%Y Cf. A296176, A296171, A296173, A296175.
%K sign
%O 1,2
%A _Paul D. Hanna_, Dec 07 2017
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