%I A059419
%S A059419 1,0,1,2,0,1,0,8,0,1,16,0,20,0,1,0,136,0,40,0,1,272,0,616,0,70,0,1,0,
%T A059419 3968,0,2016,0,112,0,1,7936,0,28160,0,5376,0,168,0,1,0,176896,0,135680,
%U A059419 0,12432,0,240,0,1,353792,0,1805056,0,508640,0,25872,0,330,0,1,0
%N A059419 Triangle T(n,k) (1<=k<=n) of tangent numbers, read by rows: T(n,k) = 
               coefficient of x^n/n! in expansion of (tan x)^k/k!.
%D A059419 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 259.
%F A059419 T(n+1, k) = T(n, k-1) + k*(k+1)*T(n, k+1), T(n, n) = 1.
%e A059419 1; 0,1; 2,0,1; 0,8,0,1; 16,0,20,0,1; ...
%o A059419 (PARI) T(n,k)=if(k<1|k>n,0,n!*polcoeff(tan(x+x*O(x^n))^k/k!,n))
%Y A059419 Diagonals give A000182, A024283, A059420 (interspersed with 0's), also 
               A007290, A059421. Row sums give A006229. Essentially the same triangle 
               as A008308.
%Y A059419 A111593 (signed triangle with extra column k=0 and row n=0).
%Y A059419 Sequence in context: A095403 A011328 A048277 this_sequence A049218 A154469 
               A022902
%Y A059419 Adjacent sequences: A059416 A059417 A059418 this_sequence A059420 A059421 
               A059422
%K A059419 nonn,easy,nice,tabl
%O A059419 1,4
%A A059419 N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2001
%E A059419 More terms from Larry Reeves (larryr(AT)acm.org), Feb 01 2001