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

0,2

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.

Links

Table of n, a(n) for n=0..15.

Formula

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

Prog

 (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)}

Crossrefs

Cf. A201731, A000629.

Sequence in context: A336217 A226837 A152684 * A260656 A141074 A351052

Adjacent sequences: A201729 A201730 A201731 * A201733 A201734 A201735

Keyword

nonn

Author

Paul D. Hanna, Dec 04 2011

Status

approved