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A003721 E.g.f. tan(tanh(x)) (odd powers only).
(Formerly M4571)
4
1, 0, -8, 112, -128, -109824, 8141824, -353878016, -9666461696, 5151942574080, -825073851170816, 76429076694827008, 2051308253366714368, -2361338488910424047616, 171581865952588387581952 (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

Table of n, a(n) for n=0..14.

FORMULA

a(n) = sum(i=0..(n-1), ((sum(j=1..2*i+1, j!*2^(2*i+1-j-1)*(-1)^(i+j+1)*Stirling2(2*i+1,j)))*sum(k=2*i+1..2*n-1, binomial(k-1,2*i)*k!*(-1)^(1+k)*2^(2*n-k-1)*Stirling2(2*n-1,k)))/(2*i+1)!). - Vladimir Kruchinin, Jun 10 2011

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[Tan[Tanh[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Nov 05 2011 *)

PROG

(Maxima)

a(n):=sum(((sum(j!*2^(2*i+1-j-1)*(-1)^(i+j+1)*stirling2(2*i+1, j), j, 1, 2*i+1))*sum(binomial(k-1, 2*i)*k!*(-1)^(1+k)*2^(2*n-k-1)*stirling2(2*n-1, k), k, 2*i+1, 2*n-1))/(2*i+1)!, i, 0, (n-1)); /* Vladimir Kruchinin, Jun 10 2011 */

CROSSREFS

Sequence in context: A079660 A131621 A239754 * A281951 A316179 A305765

Adjacent sequences:  A003718 A003719 A003720 * A003722 A003723 A003724

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

STATUS

approved

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Last modified May 8 09:57 EDT 2021. Contains 343666 sequences. (Running on oeis4.)