A294332 G.f.: exp( Sum_{n>=1} A180563(n) * x^n / n ).

1, 1, -1, 5, -45, 609, -11141, 257281, -7170355, 233936995, -8744103079, 368479396171, -17288353555771, 894005702731735, -50527305282004435, 3099060459670425655, -205028564671300495120, 14554510561318327509610, -1103542106915790217739110, 89009707681627448130203830, -7610129271299704960998906454, 687495658528174987634449288846, -65438091790081511530153327883206, 6545685493719560524729653911676430

Offset: 0

Author

Paul D. Hanna, Oct 28 2017

Keywords

• sign

Examples

			G.f.: A(x) = 1 + x - x^2 + 5*x^3 - 45*x^4 + 609*x^5 - 11141*x^6 + 257281*x^7 - 7170355*x^8 + 233936995*x^9 - 8744103079*x^10 +...
such that
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 +...+ A180563(n)*x^n/n +...
where the e.g.f. G(x) of A180563 begins
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! +...+ A180563(n)*x^n/n! +...
and satisfies: Product_{n>=1} (1 - G(x)^n) = exp(-x).
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A180653, A294331 (variant).

Programs

PARI

{A180563(n) = my( L = sum(m=1, n, sigma(m) * x^m/m ) +x*O(x^n) ); n!*polcoeff( serreverse(L), n)}
{a(n) = my(A); A = exp( sum(m=1, n+1, A180563(m)*x^m/m +x*O(x^n)) ); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))