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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

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

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

Cf. A003709, A003711.

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 5 06:15 EST 2022. Contains 358578 sequences. (Running on oeis4.)