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A003705 E.g.f. tan(sin(x)) (odd powers only).
(Formerly M3172)
5
1, 1, -3, -107, -1095, 41897, 3027637, 34528445, -11832720271, -1190157296815, 22592230600813, 23107531656941541, 2633888933338158633, -362759000929143575815, -189312598480126813670107, -18315162183020706728157939 (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
FORMULA
a(n) = 2*sum(m=0..n-1, ((sum(j=1..2*m+1, j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1,j)))*sum(i=0..(2*m+1)/2, (2*i-(2*m+1))^(2*n-1)*binomial(2*m+1,i)*(-1)^(n-i)))/(2*m+1)!). [Vladimir Kruchinin, Jun 11 2011]
MATHEMATICA
With[{nn = 50}, Take[CoefficientList[Series[Tan[Sin[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Vincenzo Librandi, Apr 11 2014 *)
PROG
(Maxima)
a(n):=2*sum(((sum(j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1, j), j, 1, 2*m+1))*sum((2*i-(2*m+1))^(2*n-1)*binomial(2*m+1, i)*(-1)^(n-i), i, 0, (2*m+1)/2))/(2*m+1)!, m, 0, n-1); /* Vladimir Kruchinin, Jun 11 2011 */
CROSSREFS
Sequence in context: A142509 A023325 A094200 * A146214 A261997 A362056
KEYWORD
sign
AUTHOR
EXTENSIONS
Changed offset from 1 to 0 by Vincenzo Librandi, Apr 11 2014
STATUS
approved

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Last modified February 23 01:10 EST 2024. Contains 370265 sequences. (Running on oeis4.)