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

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

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

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

Programs

Mathematica

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

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 */

Formula

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

Extensions

Extended and formatted by Olivier Gérard, Mar 15 1997

Name corrected by Joerg Arndt, Apr 23 2011