A012610 Expansion of e.g.f. exp(arcsinh(x)*tan(x)) (even powers only).

1, 2, 16, 350, 12248, 734218, 55640396, 6572508462, 822057317136, 170181011188626, 28436167156754964, 10592613470009612406, 1668642302509175576856, 1486955058235797307115866, 7689153648829475517246236, 472651116807461744585332416574, -170571204803370595086655592041440

Offset

0,2

Comments

a(16) is negative. - Vaclav Kotesovec, Oct 31 2013

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

Formula

a(n) ~ (-1)^(n+1) * tanh(1) * 2^(2*n) *n^(2*n-1) / exp(2*n+Pi*tanh(1)/2). - Vaclav Kotesovec, Oct 31 2013

Example

exp(arcsinh(x)*tan(x)) = 1 + 2/2!*x^2 + 16/4!*x^4 + 350/6!*x^6 + 12248/8!*x^8 ...

Mathematica

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

Prog

(PARI) seq(n)={my(x='x+O('x^(2*n))); my(v=Vec(serlaplace(exp(asinh(x)*tan(x))))); vector(n, i, v[2*i-1])} \\ Andrew Howroyd, Feb 25 2018

Crossrefs

Sequence in context: A268560 A275854 A299907 * A012721 A297095 A289972

Adjacent sequences: A012607 A012608 A012609 * A012611 A012612 A012613

Keyword

sign

Author

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

Extensions

a(14)-a(16) from Andrew Howroyd, Feb 25 2018

Status

approved