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

1,3

Comments

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

Links

Table of n, a(n) for n=1..31.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A064190, A000182, A000354.

Sequence in context: A059182 A027958 A293942 * A119283 A151499 A057781

Adjacent sequences: A064667 A064668 A064669 * A064671 A064672 A064673

Keyword

easy,nice,nonn,tabl

Author

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

Extensions

More terms from Philippe Deléham, Sep 22 2005

Status

approved