A158107 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*L(n)*x^n/n ) where Sum_{n>=1} L(n)*x^n/n = log(1+x*A(x)).

1, 1, 2, 7, 44, 272, 3053, 25670, 368728, 4867442, 86339238, 1071067999, 28751805809, 417861397848, 9791134239124, 235308903842756, 7238087265282704, 133575559401222741, 5068916834663575735

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

G.f.: A(x) = Product_{n>=1} G_{n}(x^n) where G_{n}(x^n) = Product_{k=0..n-1} [1 + u^k*x * A(u^k*x)] with u = exp(2*Pi*I/n).

Example

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 272*x^5 + 3053*x^6 +...
log(1+x*A(x)) = x + x^2/2 + 4*x^3/3 + 21*x^4/4 + 186*x^5/5 + 1366*x^6/6 +...
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 147*x^4/4 + 1116*x^5/5 + 16392*x^6/6 +...
log(A(x)) = x + 3*1*x^2/2 + 4*4*x^3/3 + 7*21*x^4/4 + 6*186*x^5/5 + 12*1366*x^6/6 +...

Prog

(PARI) {a(n)=local(A=1+x); if(n==0, 1, for(i=1, n, A=exp(sum(m=1, n, sigma(m)*x^m*polcoeff(log(1+x*A+x*O(x^m)), m))+x*O(x^n))); polcoeff(A, n))}

Crossrefs

Cf. A158108.

Sequence in context: A270580 A103084 A041507 * A145073 A111561 A000155

Adjacent sequences: A158104 A158105 A158106 * A158108 A158109 A158110

Keyword

nonn

Author

Paul D. Hanna, Mar 28 2009

Status

approved