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 A003717 Expansion of e.g.f. sin(tanh(x)) (odd powers only). (Formerly M3143) 6
 1, -3, 37, -959, 41641, -2693691, 241586893, -28607094455, 4315903789009, -807258131578995, 183184249105857781, -49548882107764546223, 15742588857552887269753, -5802682207845642276301995 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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) = (-1)^(n-1)*b(2*n-1), b(n) = sum(k=1..n,(1-(-1)^k)/k!*((-1)^(n-k)+1)* sum(j=k..n, binomial(j-1,k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)* Stirling2(n,j))). - Vladimir Kruchinin, Apr 21 2011 MATHEMATICA Sin[ Tanh[ x ] ] (* Odd Part *) With[{nn = 60}, Take[CoefficientList[Series[Sin[Tanh[x]], {x, 0, nn}], x] Range[0, nn - 1]!, {2, -1, 2}]] (* Vincenzo Librandi, Apr 11 2014 *) PROG (Maxima) a(n):=(-1)^(n-1)*b(2*n-1); b(n):=sum((1-(-1)^k)/k!*((-1)^(n-k)+1)*sum(binomial(j-1, k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)*stirling2(n, j), j, k, n), k, 1, n); /* Vladimir Kruchinin, Apr 21 2011 */ CROSSREFS Sequence in context: A143639 A143412 A331656 * A201697 A274308 A318224 Adjacent sequences:  A003714 A003715 A003716 * A003718 A003719 A003720 KEYWORD sign AUTHOR EXTENSIONS Name edited by Michel Marcus, Jan 28 2018 STATUS approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)