A012024 E.g.f. sinh(sin(arctan(x))) (odd powers only).

1, -2, 16, -104, -20096, 4427776, -954111872, 243390205696, -75389245067264, 28248828019830784, -12669814369258471424, 6721694045416881553408, -4170436153219300846567424, 2994608522937575414450814976

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Formula

a(n) = ((2*n+1)!*sum(m=0..n, C(n-1/2,n-m)*(-1)^(n-m)/(2*m+1)!)). - Vladimir Kruchinin, Jun 16 2011

a(n) = -2*(6*n^2 - 6*n + 1)*a(n-1) - 12*(n-1)^2*(2*n-3)*(2*n-1)*a(n-2) - 4*(n-2)*(n-1)*(2*n-5)*(2*n-3)^2*(2*n-1)*a(n-3). - Vaclav Kotesovec, Nov 09 2013

Lim sup n->infinity |a(n)|/(2^(2*n+5/3) * exp(3/4*(2*n)^(1/3)-2*n) * n^(2*n+2/3) / sqrt(3)) = 1. - Vaclav Kotesovec, Nov 09 2013

Example

sinh(sin(arctan(x))) = x-2/3!*x^3+16/5!*x^5-104/7!*x^7-20096/9!*x^9...

Mathematica

Table[n!*SeriesCoefficient[Sinh[x/Sqrt[1+x^2]], {x, 0, n}], {n, 1, 41, 2}] (* Vaclav Kotesovec, Nov 08 2013 *)

Prog

(Maxima)
a(n):=((2*n+1)!*sum(binomial(n-1/2, n-m)*(-1)^(n-m)/(2*m+1)!, m, 0, n)); [Vladimir Kruchinin, Jun 16 2011]

Crossrefs

Sequence in context: A187248 A236958 A009619 * A349008 A366635 A193217

Adjacent sequences: A012021 A012022 A012023 * A012025 A012026 A012027

Keyword

sign

Author

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

Status

approved