A201732 a(n) = [x^n/n!] (1/x) * log( (n+1 - n*exp(x)) / (n+2 - (n+1)*exp(x)) ).

1, 2, 18, 386, 15150, 946082, 86148762, 10776331778, 1773210244230, 371367615732002, 96462262816769586, 30433572793375652738, 11463680237091180885150, 5081782052880868302982562, 2618864991559576227420716490, 1552537179057766207300655437826

Offset: 0

Author

Paul D. Hanna, Dec 04 2011

Keywords

• nonn

Comments

The function log((n+1 - n*exp(x))/(n+2 - (n+1)*exp(x))) equals the (n+1)-th iteration of log(1/(2-exp(x))), the e.g.f. of A000629 (with offset 1), where A000629(n) is the number of necklaces of partitions of n+1 labeled beads.

Crossrefs

Cf. A201731, A000629.

Programs

PARI

{a(n)=n!*polcoeff((1/x)*log((n+1 - n*exp(x+O(x^(n+2))))/(n+2 - (n+1)*exp(x+O(x^(n+2))))),n)}

Formula

a(n) = A201731(n+1) / (n+1).