A294331 G.f.: exp( Sum_{n>=1} A294330(n) * x^n / n ).

1, 1, 2, 8, 60, 732, 12672, 283704, 7757526, 249885110, 9255184676, 387336669496, 18075315527932, 930651571119228, 52411013929403760, 3205007479811374344, 211500660045169230729, 14981245823696876792553, 1133747667225683826679642, 91294225766212875597830080, 7793993663152146113116892960, 703185550242112366418746032320, 66853101136423829966807930994240

Offset: 0

Author

Paul D. Hanna, Oct 28 2017

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 60*x^4 + 732*x^5 + 12672*x^6 + 283704*x^7 + 7757526*x^8 + 249885110*x^9 + 9255184676*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 +...+ A294330(n)*x^n/n +...
where the e.g.f. G(x) of A294330 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! +...+ A294330(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. A294330.

Programs

PARI

{A294330(n) = my( L = sum(m=1, n, (-1)^(m-1) * 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, A294330(m)*x^m/m +x*O(x^n)) ); polcoeff(A,n)}
for(n=0, 25, print1(a(n), ", "))

Formula

a(n) ~ c * d^n * n^(n-2), where d = 1.788680223969315995... and c = 0.254472375755339325... - Vaclav Kotesovec, Oct 29 2017