A064190 Triangle T(n,k) generalizing the tangent numbers.

1, 2, 6, 16, 48, 72, 272, 816, 1440, 1440, 7936, 23808, 44352, 57600, 43200, 353792, 1061376, 2027520, 2903040, 3024000, 1814400, 22368256, 67104768, 129964032, 195379200, 232243200, 203212800, 101606400, 1903757312, 5711271936

Offset: 0

Author

N. J. A. Sloane, Sep 21 2001

Keywords

• nonn
• tabl
• easy
• nice

Examples

			Triangle begins:
    1;
    2,   6;
   16,  48,   72;
  272, 816, 1440, 1440;
  ...
		

Links

• J. L. Arregui, Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles, arXiv:math/0109108 [math.NT], 2001.

Crossrefs

First column gives A000182.

If m*(m+1) is replaced in the formula by m*m, the first column is the sequence of secant numbers A000364. - Jose L. Arregui (arregui(AT)posta.unizar.es), Oct 09 2001

Programs

Mathematica

t[1, 1] = 1; t[1, 0] = 0; t[n_ /; n > 1, m_] := t[n, m] = m*(m+1)*Sum[t[n-1, k], {k, m-1, n-1}]; Table[t[n, k], {n, 1, 8}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jan 02 2013 *)

Formula

T(n+1, m) = m*(m+1)*Sum_{k = m-1..n} T(n, k).

Extensions

More terms from Vladeta Jovovic, Sep 22 2001