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

%I M4453

%S 1,-1,-7,-97,-2063,-53409,-752343,166831871,43685848289,9398558916159,

%T 2116926930779225,524586454143030495,144620290378876829905,

%U 44287070229737735633567,14954349885478653319004041

%N E.g.f. cos(tan(x)) (even powers only).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%F 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

%t 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 *)

%o (Maxima)

%o 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 */

%K sign

%O 0,3

%A _R. H. Hardin_, _Simon Plouffe_

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)