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

%I A064190 #17 Dec 26 2023 18:25:42
%S A064190 1,2,6,16,48,72,272,816,1440,1440,7936,23808,44352,57600,43200,353792,
%T A064190 1061376,2027520,2903040,3024000,1814400,22368256,67104768,129964032,
%U A064190 195379200,232243200,203212800,101606400,1903757312,5711271936
%N A064190 Triangle T(n,k) generalizing the tangent numbers.
%H A064190 J. L. Arregui, <a href="https://arxiv.org/abs/math/0109108">Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles</a>, arXiv:math/0109108 [math.NT], 2001.
%F A064190 T(n+1, m) = m*(m+1)*Sum_{k = m-1..n} T(n, k).
%e A064190 Triangle begins:
%e A064190     1;
%e A064190     2,   6;
%e A064190    16,  48,   72;
%e A064190   272, 816, 1440, 1440;
%e A064190   ...
%t A064190 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 *)
%Y A064190 First column gives A000182.
%Y A064190 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
%K A064190 nonn,tabl,easy,nice
%O A064190 0,2
%A A064190 _N. J. A. Sloane_, Sep 21 2001
%E A064190 More terms from _Vladeta Jovovic_, Sep 22 2001