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 A003706 E.g.f. sin(tan(x)), zeros omitted. (Formerly M3176) 7
 1, 1, -3, -275, -15015, -968167, -77000363, -7433044411, -843598411471, -107426835190735, -14072980460605907, -1424712499632406371, 164163646840636339593, 237037449673450822122569, 155015924346163216960553093, 92387809011599803660871724021 (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 Vladimir V. Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013. FORMULA a(n) = b(2*n-1), b(n) = sum(k=1..n, ((-1)^(n-k)+1)*sum(j=k..n, binomial(j-1,k-1)*j!*2^(n-j-1)*(-1)^((n+k)/2+j)*stirling2(n,j))*((-1)^((k+3)/2)-(-1)^((3*k+3)/2))/(2*k!)). - Vladimir Kruchinin, Apr 23 2011 a(n) = sum(m=0..n, sum(j=0..2*n-2*m, binomial(j+2*m,2*m)*(j+2*m+1)!*2^(2*n-2*m-j)*(-1)^(n+j)* stirling2(2*n+1,j+2*m+1))/((2*m+1)!)). - Vladimir Kruchinin, Jan 21 2012 MATHEMATICA With[{nn=50}, Take[CoefficientList[Series[Sin[Tan[x]], {x, 0, nn}], x] Range[ 0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jul 25 2012 *) PROG (Maxima) a(n):=b(2*n-1); b(n):=sum(((-1)^(n-k)+1)*sum(binomial(j-1, k-1)*j!*2^(n-j-1)*(-1)^((n+k)/2+j)*stirling2(n, j), j, k, n)*((-1)^((k+3)/2)-(-1)^((3*k+3)/2))/(2*k!), k, 1, n); /* Vladimir Kruchinin, Apr 23 2011 */ a(n):=sum(sum(binomial(j+2*m, 2*m)*(j+2*m+1)!*2^(2*n-2*m-j)*(-1)^(n+j)*stirling2(2*n+1, j+2*m+1), j, 0, 2*n-2*m)/((2*m+1)!), m, 0, n); /* Vladimir Kruchinin, Jan 21 2012 */ CROSSREFS Sequence in context: A171358 A115477 A051365 * A068250 A364617 A263884 Adjacent sequences: A003703 A003704 A003705 * A003707 A003708 A003709 KEYWORD sign AUTHOR R. H. Hardin, Simon Plouffe EXTENSIONS Corrected name, Joerg Arndt, Apr 23 2011 More terms from Harvey P. Dale, Jul 25 2012 STATUS approved

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Last modified April 17 11:00 EDT 2024. Contains 371763 sequences. (Running on oeis4.)