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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: A245265 A143639 A143412 * A201697 A274308 A318224

Adjacent sequences:  A003714 A003715 A003716 * A003718 A003719 A003720

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

EXTENSIONS

Name edited by Michel Marcus, Jan 28 2018

STATUS

approved

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Last modified October 20 19:44 EDT 2018. Contains 316401 sequences. (Running on oeis4.)