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 A003705 E.g.f. tan(sin(x)) (odd powers only). (Formerly M3172) 5
 1, 1, -3, -107, -1095, 41897, 3027637, 34528445, -11832720271, -1190157296815, 22592230600813, 23107531656941541, 2633888933338158633, -362759000929143575815, -189312598480126813670107, -18315162183020706728157939 (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 Vincenzo Librandi, Table of n, a(n) for n = 0..100 FORMULA 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] MATHEMATICA 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 *) PROG (Maxima) 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 */ CROSSREFS Sequence in context: A142509 A023325 A094200 * A146214 A261997 A362056 Adjacent sequences: A003702 A003703 A003704 * A003706 A003707 A003708 KEYWORD sign AUTHOR R. H. Hardin, Simon Plouffe EXTENSIONS Changed offset from 1 to 0 by Vincenzo Librandi, Apr 11 2014 STATUS approved

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Last modified February 23 01:10 EST 2024. Contains 370265 sequences. (Running on oeis4.)