|
|
A003710
|
|
Expansion of e.g.f. cos(tan(x)) (even powers only).
(Formerly M4453)
|
|
6
|
|
|
1, -1, -7, -97, -2063, -53409, -752343, 166831871, 43685848289, 9398558916159, 2116926930779225, 524586454143030495, 144620290378876829905, 44287070229737735633567, 14954349885478653319004041
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2 * Sum_{m=0..n} ( Sum_{j=2*m..2*n} binomial(j-1,2*m-1) * j! * 2^(2*n-j-1) * (-1)^(n+j) * Stirling2(2*n,j) )/(2*m)!, n>0, a(0)=1. - Vladimir Kruchinin, Jun 29 2011
|
|
MATHEMATICA
|
nn = 20; Table[(CoefficientList[Series[Cos[Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 16 2015 *)
|
|
PROG
|
(Maxima) a(n):=if n=0 then 1 else 2*sum((sum(binomial(j-1, 2*m-1)*j!*2^(2*n-j-1)*(-1)^(n+j)*stirling2(2*n, j), j, 2*m, 2*n))/(2*m)!, m, 0, n); /* Vladimir Kruchinin, Jun 28 2011 */
(PARI) my(x='x+O('x^30)); select(x->x, Vec(serlaplace(cos(tan(x))))) \\ Michel Marcus, Oct 02 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|