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

0,2

Links

Table of n, a(n) for n=0..29.

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

Formula

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

Example

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

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 *)

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

Sequence in context: A071726 A148443 A148444 * A151281 A045694 A225178

Adjacent sequences: A064187 A064188 A064189 * A064191 A064192 A064193

Keyword

nonn,tabl,easy,nice

Author

N. J. A. Sloane, Sep 21 2001

Extensions

More terms from Vladeta Jovovic, Sep 22 2001

Status

approved