A008308 - OEIS

%I #15 Dec 17 2021 05:38:47

%S 1,1,2,1,8,1,16,20,1,136,40,1,272,616,70,1,3968,2016,112,1,7936,28160,

%T 5376,168,1,176896,135680,12432,240,1,353792,1805056,508640,25872,330,

%U 1,11184128,11977856,1595264,49632,440,1,22368256,154918400,59835776

%N Triangle of tangent numbers.

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 259.

%e Triangle begins:

%e     1;

%e     1;

%e     2,  1;

%e     8,  1;

%e    16, 20, 1;

%e   136, 40, 1;

%e   ...

%t T[n_, n_] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = T[n - 1, k - 1] + k*(k + 1)*T[n - 1, k + 1]; T[_, _] = 0;

%t row[n_] := DeleteCases[Table[T[n, k], {k, 1, n}] , 0];

%t Array[row, 13] // Flatten (* _Jean-François Alcover_, Nov 09 2017 *)

%Y Essentially the same triangle as A059419, which is the main entry for this triangle.

%Y Row sums give A006229.

%K tabf,nonn,nice

%O 1,3

%A _N. J. A. Sloane_

%E More terms from Larry Reeves (larryr(AT)acm.org), Feb 08 2001