A294332 - OEIS

%I #6 Oct 28 2017 10:02:05

%S 1,1,-1,5,-45,609,-11141,257281,-7170355,233936995,-8744103079,

%T 368479396171,-17288353555771,894005702731735,-50527305282004435,

%U 3099060459670425655,-205028564671300495120,14554510561318327509610,-1103542106915790217739110,89009707681627448130203830,-7610129271299704960998906454,687495658528174987634449288846,-65438091790081511530153327883206,6545685493719560524729653911676430

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

%H Paul D. Hanna, <a href="/A294332/b294332.txt">Table of n, a(n) for n = 0..300</a>

%e 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 +...

%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 +...+ A180563(n)*x^n/n +...

%e where the e.g.f. G(x) of A180563 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! +...+ A180563(n)*x^n/n! +...

%e and satisfies: Product_{n>=1} (1 - G(x)^n) = exp(-x).

%o (PARI) {A180563(n) = my( L = sum(m=1, n, 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, A180563(m)*x^m/m +x*O(x^n)) ); polcoeff(A, n)}

%o for(n=0, 25, print1(a(n), ", "))

%Y Cf. A180653, A294331 (variant).

%K sign

%O 0,4

%A _Paul D. Hanna_, Oct 28 2017