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 A009710 E.g.f. tan(tan(x)^2) (even powers only). 2
 0, 2, 16, 512, 34816, 3821312, 618121216, 138682959872, 41171702972416, 15610723195092992, 7357121913006063616, 4217775794187229724672, 2889975739296119171055616, 2332177121915783600628826112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..13. FORMULA a(n)=4*sum(m=0..n-1/2, ((sum(j=1..2*m+1, j!*2^(2*m-j)*(-1)^(m+1+j)*stirling2(2*m+1,j)))*sum(j=4*m+2..2*n, binomial(j-1,4*m+1)*j!*2^(2*n-j-1)*(-1)^(n+1+j)*stirling2(2*n,j)))/(2*m+1)!). [Vladimir Kruchinin, Jun 21 2011] a(n) ~ (2*n)! * 2 * sqrt(2) / ((2+Pi) * sqrt(Pi) * arctan(sqrt(Pi/2))^(2*n+1)). - Vaclav Kotesovec, Jan 24 2015 EXAMPLE tan(tan(x)*tan(x))=2/2!*x^2+16/4!*x^4+512/6!*x^6+34816/8!*x^8... MATHEMATICA nn = 20; Table[(CoefficientList[Series[Tan[Tan[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 24 2015 *) PROG (Maxima) a(n):=4*sum(((sum(j!*2^(2*m-j)*(-1)^(m+1+j)*stirling2(2*m+1, j), j, 1, 2*m+1))*sum(binomial(j-1, 4*m+1)*j!*2^(2*n-j-1)*(-1)^(n+1+j)*stirling2(2*n, j), j, 4*m+2, 2*n))/(2*m+1)!, m, 0, n-1/2); [Vladimir Kruchinin, Jun 21 2011] CROSSREFS Sequence in context: A168403 A140311 A012389 * A012393 A189899 A189335 Adjacent sequences: A009707 A009708 A009709 * A009711 A009712 A009713 KEYWORD nonn AUTHOR R. H. Hardin EXTENSIONS Extended and signs tested Mar 15 1997 by Olivier Gérard. STATUS approved

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Last modified June 5 07:03 EDT 2023. Contains 363130 sequences. (Running on oeis4.)