login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A245153 E.g.f.: (cosh(x) + sinh(x)*cosh(3*x)) / sqrt(1 - sinh(x)^2*sinh(3*x)^2). 4
1, 1, 1, 28, 109, 1036, 12421, 189568, 2377369, 50888656, 889772041, 21056972608, 463426778629, 13171920918976, 338302052475661, 11024635871323648, 331174000888419889, 12111179923298826496, 413871819030803915281, 16886967133601994738688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Limit (a(n)/n!)^(-1/n) = log( (1+sqrt(5))/2 ) = 0.4812118250596...

LINKS

Table of n, a(n) for n=0..19.

FORMULA

E.g.f.: G(x) * (cosh(3*x) - sinh(3*x)*cosh(x)) / sqrt(1 - sinh(x)^2*sinh(3*x)^2), where G(x) is the e.g.f. of A245155.

a(n) ~ sqrt(2) * n^n / (5^(1/4) * exp(n) * (log((1+sqrt(5))/2))^(n+1/2)). - Vaclav Kotesovec, Nov 04 2014

EXAMPLE

E.g.f.: A(x) = 1 + x + x^2/2! + 28*x^3/3! + 109*x^4/4! + 1036*x^5/5! +...

Let A(x) = A0(x) + A1(x) where

A0(x) = 1 + x^2/2! + 109*x^4/4! + 12421*x^6/6! + 2377369*x^8/8! +...

A1(x) = x + 28*x^3/3! + 1036*x^5/5! + 189568*x^7/7! + 50888656*x^9/9! +...

then A0(x)^2 - A1(x)^2 = 1.

Note that the logarithm of the e.g.f. is an odd function:

Log(A(x)) = x + 27*x^3/3! + 765*x^5/5! + 121527*x^7/7! + 29881305*x^9/9! + 11156851827*x^11/11! + 6479306260245*x^13/13! +...

thus A(x)*A(-x) = 1.

PROG

(PARI) {a(n)=local(X=x+x^2*O(x^n)); n!*polcoeff((cosh(X) + sinh(X)*cosh(3*X)) / sqrt(1 - sinh(X)^2*sinh(3*X)^2), n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A245154, A245155, A245138, A245164.

Sequence in context: A044660 A183341 A118613 * A295981 A064763 A219594

Adjacent sequences:  A245150 A245151 A245152 * A245154 A245155 A245156

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 12 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 19:59 EST 2019. Contains 329288 sequences. (Running on oeis4.)