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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A009015 Expansion of E.g.f.: cos(x*cos(x)) (even powers only). 8
 1, -1, 13, -181, 3865, -140521, 6324517, -344747677, 23853473329, -1996865965009, 193406280000061, -21615227339380357, 2778071540350106953, -403985610499148666041, 65635628800688339178325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..250 FORMULA a(n) = Sum_{j=0..(2*n-1)/2} binomial(2*n,2*j)*((Sum_{i=0..((2*j-1)/2)} (j-i)^(2*n-2*j)*binomial(2*j,i)))*(-1)^(n))/(2^(4*j-2*n-1)))+(-1)^n. - Vladimir Kruchinin, Jun 06 2011 MAPLE seq(coeff(series(factorial(n)*(cos(x*cos(x))), x, n+1), x, n), n=0..30, 2); # Muniru A Asiru, Jul 21 2018 MATHEMATICA With[{nmax = 60}, CoefficientList[Series[Cos[x*Cos[x]], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]] (* G. C. Greubel, Jul 21 2018 *) PROG (Maxima) a(n):=sum(binomial(2*n, 2*j)*((sum((j-i)^(2*n-2*j)*binomial(2*j, i), i, 0, ((2*j-1)/2)))*(-1)^(n))/(2^(4*j-2*n-1)), j, 0, (2*n-1)/2)+(-1)^n; /* Vladimir Kruchinin, Jun 06 2011 */ (PARI) x='x+O('x^50); v=Vec(serlaplace(cos(x*cos(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Jul 21 2018 CROSSREFS Sequence in context: A001570 A239902 A020544 * A067385 A097260 A178303 Adjacent sequences: A009012 A009013 A009014 * A009016 A009017 A009018 KEYWORD sign AUTHOR R. H. Hardin EXTENSIONS Extended with signs by Olivier Gérard, Mar 15 1997 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.

Last modified December 6 18:25 EST 2023. Contains 367614 sequences. (Running on oeis4.)