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A003705 E.g.f. tan(sin(x)) (odd powers only).
(Formerly M3172)
4

%I M3172

%S 1,1,-3,-107,-1095,41897,3027637,34528445,-11832720271,-1190157296815,

%T 22592230600813,23107531656941541,2633888933338158633,

%U -362759000929143575815,-189312598480126813670107,-18315162183020706728157939

%N E.g.f. tan(sin(x)) (odd powers only).

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

%H Vincenzo Librandi, <a href="/A003705/b003705.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = 2*sum(m=0..n-1, ((sum(j=1..2*m+1, j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1,j)))*sum(i=0..(2*m+1)/2, (2*i-(2*m+1))^(2*n-1)*binomial(2*m+1,i)*(-1)^(n-i)))/(2*m+1)!). [_Vladimir Kruchinin_, Jun 11 2011]

%t With[{nn = 50}, Take[CoefficientList[Series[Tan[Sin[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* _Vincenzo Librandi_, Apr 11 2014 *)

%o (Maxima)

%o a(n):=2*sum(((sum(j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1,j),j,1,2*m+1))*sum((2*i-(2*m+1))^(2*n-1)*binomial(2*m+1,i)*(-1)^(n-i),i,0,(2*m+1)/2))/(2*m+1)!,m,0,n-1); /* _Vladimir Kruchinin_, Jun 11 2011 */

%K sign

%O 0,3

%A _R. H. Hardin_, _Simon Plouffe_

%E Changed offset from 1 to 0 by _Vincenzo Librandi_, Apr 11 2014

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Last modified September 19 08:05 EDT 2021. Contains 347556 sequences. (Running on oeis4.)