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

 

Logo

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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003711 Expansion of e.g.f. cos(tanh(x)) (even powers only).
(Formerly M4665)
6
1, -1, 9, -177, 6097, -325249, 24807321, -2558036145, 342232522657, -57569080467073, 11879658510739497, -2948163649552594737, 865683568087537789297, -296699416391356495667713, 117330699580950022391960505 (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

Seiichi Manyama, Table of n, a(n) for n = 0..100

FORMULA

a(n) = Sum_{m=1..n} ( Sum_{k=0..2*n-2*m} binomial(2*m+k-1,2*m-1) * (2*m+k)! * (-1)^k * 2^(2*n-2*m-k) * Stirling2(2*n,2*m+k) )/(2*m)!, n>0, a(0)=1. - Vladimir Kruchinin, Jun 10 2011

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Cos[Tanh[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):=sum((sum(binomial(2*m+k-1, 2*m-1)*(2*m+k)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n, 2*m+k), k, 0, 2*n-2*m))/(2*m)!, m, 1, n); /* Vladimir Kruchinin, Jun 10 2011 */

CROSSREFS

Cf. A003710.

Sequence in context: A157774 A232694 A193443 * A009009 A220267 A304402

Adjacent sequences: A003708 A003709 A003710 * A003712 A003713 A003714

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

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 December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)