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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
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
KEYWORD
sign
AUTHOR
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.)