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A064190 Triangle T(n,k) generalizing the tangent numbers. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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.

FORMULA

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

EXAMPLE

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-Fran├žois 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

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Last modified October 19 17:55 EDT 2018. Contains 316376 sequences. (Running on oeis4.)