A009567 Expansion of e.g.f.: sinh(log(1 + sin(x))).

0, 1, -1, 2, -8, 31, -136, 692, -3968, 25261, -176896, 1351382, -11184128, 99680491, -951878656, 9695756072, -104932671488, 1202439837721, -14544442556416, 185185594118762, -2475749026562048, 34674437196568951

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Comments

|a(n)| = number of odd alternating permutations on n letters (offset 1). - Vladeta Jovovic, May 20 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A000111, A009123.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Sinh[Log[1+Sin[x]]],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, May 11 2014 *)

PARI

x='x+O('x^30); concat([0], Vec(serlaplace(sinh(log(1+sin(x)))))) \\ G. C. Greubel, Jan 21 2018

Formula

a(2*n) = A000182(n+1)/2.

a(2*n+1) = A012007(n+1) - 1.

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and previous Mathematica program replaced by Harvey P. Dale, May 11 2014