A003718 E.g.f. tan(tan(x)), zeros omitted. (Formerly M3694)

1, 4, 72, 2896, 203904, 22112000, 3412366336, 709998153728, 191483931951104, 64956739430973440, 27065724289967718400, 13588059904833174896640, 8089418253144660155301888, 5634743143901240164716904448, 4539998748622480932947483426816

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 0..50

Formula

a(n) ~ 8 * (2*n+1)! / ((4+Pi^2) * (arctan(Pi/2))^(2*n+2)). - Vaclav Kotesovec, Feb 16 2015

Mathematica

Rest@ Union[ Range[0, 29]! CoefficientList[ Series[ Tan@ Tan@ x, {x, 0, 29}], x]] (* Robert G. Wilson v, May 07 2011 *)

Prog

(Maxima)
a(n):=b(2*n+1);
b(n):=sum((((-1)^(k-1)+1)*(sum(j!*2^(k-j-1)*(-1)^((k+1)/2+j)* stirling2(k, j), j, 1, k))*((-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))/k!, k, 1, n); /* Vladimir Kruchinin, Apr 23 2011 */

Crossrefs

Sequence in context: A309980 A266865 A327882 * A012947 A203535 A013066

Adjacent sequences: A003715 A003716 A003717 * A003719 A003720 A003721

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and formatted by Olivier Gérard, Mar 15 1997

Name corrected by Joerg Arndt, Apr 23 2011

Status

approved