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

0,4

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000111, A009123.

Sequence in context: A150816 A150817 A150818 * A150819 A003175 A129427

Adjacent sequences: A009564 A009565 A009566 * A009568 A009569 A009570

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

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

Status

approved