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A003710 E.g.f. cos(tan(x)) (even powers only).
(Formerly M4453)
4
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

Table of n, a(n) for n=0..14.

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 */

CROSSREFS

Sequence in context: A305137 A132061 A013521 * A027837 A174315 A046908

Adjacent sequences:  A003707 A003708 A003709 * A003711 A003712 A003713

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

STATUS

approved

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Last modified December 12 07:08 EST 2018. Contains 318053 sequences. (Running on oeis4.)