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A009567 Expansion of e.g.f.: sinh(log(1 + sin(x))). 3
0, 1, -1, 2, -8, 31, -136, 692, -3968, 25261, -176896, 1351382, -11184128, 99680491, -951878656, 9695756072, -104932671488, 1202439837721, -14544442556416, 185185594118762, -2475749026562048, 34674437196568951 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
|a(n)| = number of odd alternating permutations on n letters (offset 1). - Vladeta Jovovic, May 20 2007
LINKS
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
Sequence in context: A150816 A150817 A150818 * A150819 A003175 A129427
KEYWORD
sign,easy
AUTHOR
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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)