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A003705 E.g.f. tan(sin(x)) (odd powers only).
(Formerly M3172)
4
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

Vincenzo Librandi, Table of n, a(n) for n = 0..100

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 A061308

Adjacent sequences:  A003702 A003703 A003704 * A003706 A003707 A003708

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

EXTENSIONS

Changed offset from 1 to 0 by Vincenzo Librandi, Apr 11 2014

STATUS

approved

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Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)