|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|