login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A203715 E.g.f.: Sum_{n>=1} log((1 + exp(2*x^n))/2). 1
1, 3, 6, 34, 120, 1096, 5040, 56848, 362880, 5451136, 39916800, 688876288, 6227020800, 130789805056, 1307674368000, 29497569445888, 355687428096000, 9746045395173376, 121645100408832000, 3451902721622867968, 51090942171709440000, 1686006043164464644096 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..22.

FORMULA

a(2*n-1) = (2*n-1)!.

EXAMPLE

E.g.f.: A(x) = x + 3*x^2/2! + x^3 + 34*x^4/4! + x^5 + 1096*x^6/6! + x^7 + 56848*x^8/8! + x^9 + 5451136*x^10/10! + x^11 +...

where A(x) = log((1+exp(2*x))/2) + log((1+exp(2*x^2))/2) + log((1+exp(2*x^3))/2) + log((1+exp(2*x^4))/2) +...

The exponentiation of the e.g.f. begins:

exp(A(x)) = 1 + x + 4*x^2/2! + 16*x^3/3! + 104*x^4/4! + 696*x^5/5! + 6272*x^6/6! + 57856*x^7/7! + 652416*x^8/8! +...+ A203716(n)*x^n/n! +...

MATHEMATICA

nmax = 25; Rest[Range[0, nmax]! * CoefficientList[Series[Sum[Log[1/(1 - Tanh[x^k])], {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Mar 21 2016 *)

PROG

(PARI) {a(n)=n!*polcoeff(sum(m=1, n, log((1+exp(2*x^m+x*O(x^n)))/2)), n)}

CROSSREFS

Cf. A203709, A203716 (exp).

Sequence in context: A298679 A261885 A186750 * A249875 A308557 A134748

Adjacent sequences:  A203712 A203713 A203714 * A203716 A203717 A203718

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 04 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 19 09:28 EDT 2022. Contains 356227 sequences. (Running on oeis4.)