A012476 arcsinh(cos(x)*sin(x))=x-5/3!*x^3+65/5!*x^5-3005/7!*x^7+278465/9!*x^9...

1, -5, 65, -3005, 278465, -42738005, 9852460865, -3178878885005, 1367383455547265, -756164182327284005, 522662665715777337665, -441523138107985704375005, 447556468280585958726432065

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

E.g.f.: log(sin(2*x)/2+sqrt(1+(sin(2*x))^2/4)). - Vaclav Kotesovec, Oct 31 2013

a(n) ~ (-1)^n * 5^(1/4) * 2^(4*n+3/2) * n^(2*n) / (exp(2*n)*(log(2+sqrt(5)))^(2*n+1/2)). - Vaclav Kotesovec, Oct 31 2013

Mathematica

Table[n!*SeriesCoefficient[ArcSinh[Cos[x]*Sin[x]], {x, 0, n}], {n, 1, 40, 2}] (* Vaclav Kotesovec, Oct 31 2013 *)

Crossrefs

Sequence in context: A171800 A195244 A162080 * A195516 A167536 A237887

Adjacent sequences: A012473 A012474 A012475 * A012477 A012478 A012479

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved