A201224 - OEIS

A201224

E.g.f.: -log(cos(x) - x).

1, 2, 5, 20, 109, 736, 5977, 56608, 612729, 7461376, 100954061, 1502526464, 24395453861, 429099278336, 8128143367905, 164963608236032, 3571195811862385, 82142538217160704, 2000535014776893973, 51428669814460383232, 1391684597704875555165

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

a(n) ~ (n-1)!/r^n, where r = 0.73908513321516... is the root of the equation r = cos(r). - Vaclav Kotesovec, Jun 27 2013

EXAMPLE

E.g.f.: A(x) = x + 2*x^2/2! + 5*x^3/3! + 20*x^4/4! + 109*x^5/5! + 736*x^6/6! +...

such that

exp(-A(x)) = 1 - x - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10! +...

MATHEMATICA

CoefficientList[Series[-Log[Cos[x]-x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

PROG

(PARI) {a(n)=n!*polcoeff(-log(cos(x+x*O(x^n))-x), n)}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Sequence in context: A006867 A170946 A296727 * A305922 A019536 A129949

Adjacent sequences: A201221 A201222 A201223 * A201225 A201226 A201227

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 08 2012

STATUS

approved