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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 A263884 A096126

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 July 25 20:28 EDT 2021. Contains 346291 sequences. (Running on oeis4.)