A009411 Expansion of log(1+x)*cosh(log(1+x)).

0, 1, -1, 5, -24, 134, -870, 6474, -54432, 510768, -5294160, 60090480, -741407040, 9881421120, -141493322880, 2166467990400, -35323552051200, 611048958105600, -11178032634316800, 215604729694771200, -4373272831527936000

Offset

0,4

Comments

|a(n)| = number of cycles in all permutations of [n] with odd number of cycles. - Vladeta Jovovic, Sep 06 2007

a(n) is a function of the harmonic numbers. - Gary Detlefs, Jul 13 2010

Links

Robert Israel, Table of n, a(n) for n = 0..411

Formula

a(n) = (-1)^(n+1)/2*(n!*H(n)-(n-2)!), n> 1, where H(n) = sum(1/k, k=1..n). - Gary Detlefs, Jul 13 2010

Maple

H:= n-> sum(1/k, k=1..n): seq((-1)^(n+1)/2*(n!*H(n)-(n-2)!), n = 2..20); # Gary Detlefs, Jul 13 2010

Mathematica

Log[ 1+x ]*Cosh[ Log[ 1+x ] ]

Crossrefs

Cf. A000254.

Sequence in context: A066118 A002709 A193668 * A080996 A020055 A256325

Adjacent sequences: A009408 A009409 A009410 * A009412 A009413 A009414

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved