A296177 G.f. equals the logarithm of the e.g.f. of A296176.

1, -15, -6090, -30600650, -593306350650, -31192838317208826, -3652177141294409632400, -836986399841753367052602000, -342157863774785896821739864893375, -232492750600387706453977026534258393375, -248374508240426643818180115122847840121356750, -398845502818641863837604075681689663598753652620750

Offset: 1

Author

Paul D. Hanna, Dec 07 2017

Keywords

• sign

Comments

E.g.f. G(x) of A296176 satisfies: [x^(n-1)] G(x)^(n^5) = [x^n] G(x)^(n^5) for n>=1.

Examples

			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 +...
such that
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! +...
satisfies [x^(n-1)] G(x)^(n^5) = [x^n] G(x)^(n^5) for n>=1.
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 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A296176, A296171, A296173, A296175.

Programs

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)}
for(n=1,30,print1(a(n),", "))