A130461 Triangle, antidiagonals of an array generated from A130460.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 6, 4, 1, 1, 1, 2, 6, 12, 5, 1, 1, 1, 2, 6, 24, 20, 6, 1, 1, 1, 2, 6, 24, 60, 30, 7, 1, 1, 1, 2, 6, 24, 120, 120, 42, 8, 1, 1, 1, 2, 6, 24, 120, 360, 210, 56, 9, 1, 1, 1, 2, 6, 24, 120, 720, 840, 336, 72, 10, 1, 1, 1, 2, 6, 24, 120, 720, 2520

Offset

0,9

Comments

Rows tend to the factorials: (1, 1, 2, 6, 24, ...). Row sums = A130476: (1, 2, 3, 5, 8, 15, 28, 61, 132, ...).

Links

Table of n, a(n) for n=0..85.

Formula

Let A130460 = M, an infinite lower triangular matrix and V = [1, 1, 1, ...], the first row of an array. Perform M * V = second row, ...; (n+1)-th row = M * n-th row. The triangle = antidiagonals of the array.

Example

The array =
  1, 1, 1, 1,  1,   1, ...
  1, 1, 2, 3,  4,   5, ...
  1, 1, 2, 6, 12,  20, ...
  1, 1, 2, 6, 24,  60, ...
  1, 1, 2, 6, 24, 120, ...
  1, 1, 2, 6, 24, 120, ...
  ...
First few rows of the triangle:
  1;
  1, 1;
  1, 1, 1;
  1, 1, 2, 1;
  1, 1, 2, 3,  1;
  1, 1, 2, 6,  4,  1;
  1, 1, 2, 6, 12,  5,  1;
  1, 1, 2, 6, 24, 20,  6, 1;
  1, 1, 2, 6, 24, 60, 30, 7, 1;
  ...

Crossrefs

Cf. A130460, A130476, A130477, A130478.

Sequence in context: A238888 A179748 A096670 * A225631 A306209 A267482

Adjacent sequences: A130458 A130459 A130460 * A130462 A130463 A130464

Keyword

nonn,tabl

Author

Gary W. Adamson, May 28 2007

Extensions

a(23) and a(38) corrected by Gionata Neri, Jun 22 2016

Status

approved