A064670 Triangle T(n,k) (1 <= k <= n) where the first column (T(n,1)) is the sequence of secant numbers A000364.

1, 1, 4, 5, 20, 36, 61, 244, 504, 576, 1385, 5540, 11916, 17280, 14400, 50521, 202084, 442224, 697536, 792000, 518400, 2702765, 10811060, 23870196, 39202560, 50198400, 47174400, 25401600, 199360981, 797443924, 1769923944

Offset: 1

Author

Jose L. Arregui (arregui(AT)posta.unizar.es), Oct 09 2001

Keywords

• easy
• nice
• nonn
• tabl

Comments

Replacing m*m by m*(m+1) in the formula, the first column gives the tangent numbers A000182.

Examples

			T(4,3) = 9*(T(3,2) + T(3,3)) = 9*(20+36) = 504.
		

Crossrefs

Cf. A064190, A000182, A000354.

Programs

Mathematica

T[1, 1] = 1; T[n_, k_] /; 1 <= k <= n := T[n, k] = k^2*Sum[T[n-1, j], {j, k-1, n-1}]; T[, ] = 0; Table[T[n, k], {n, 1, 8}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 25 2016 *)

Formula

T(n+1, m) = m*m*Sum_{k = m-1..n} T(n, k) (T(n, 0) = 0).

Extensions

More terms from Philippe Deléham, Sep 22 2005