A129687 A129686 * A007318.

1, 1, 1, 2, 2, 1, 2, 4, 3, 1, 2, 6, 7, 4, 1, 2, 8, 13, 11, 5, 1, 2, 10, 21, 24, 16, 6, 1, 2, 12, 31, 45, 40, 22, 7, 1, 2, 14, 43, 76, 85, 62, 29, 8, 1, 2, 16, 57, 119, 161, 147, 91, 37, 9, 1, 2, 18, 73, 176, 280, 308, 238, 128, 46, 10, 1, 2, 20, 91, 249, 456

Offset: 0

Author

Gary W. Adamson, Apr 28 2007

Keywords

• nonn
• tabl

Comments

Row sums = A084215: (1, 2, 5, 10, 20, 40, 80, ...). A007318 * A129686 = A124725.

From Philippe Deléham, Feb 12 2014: (Start)

Riordan array ((1+x^2)/(1-x), x/(1-x)).

Diagonal sums are A000032(n) - 0^n (cf. A000204).

T(n,0) = A046698(n+1).

T(n+1,1) = A004277(n).

T(n+2,2) = A002061(n+1).

T(n+3,3) = A006527(n+1) = A167875(n).

T(n+4,4) = A006007(n+1).

T(n+5,5) = A081282(n+1). (End)

Examples

			First few rows of the triangle:
  1;
  1,   1;
  2,   2,   1;
  2,   4,   3,   1;
  2,   6,   7,   4,   1;
  2,   8,  13,  11,   5,   1;
  2,  10,  21,  24,  16,   6,   1;
  2,  12,  31,  45,  40,  22,   7,   1;
  2,  14,  43,  76,  85,  62,  29,   8,   1;
  2,  16,  57, 119, 161, 147,  91,  37,   9,   1;
  ...
		

Crossrefs

Cf. A129686, A007318, A124725.

Cf. Columns: A046698, A004277, A002061, A006527, A006007, A081282

Formula

A129686 * A007318 (Pascal's Triangle), as infinite lower triangular matrices.

T(n,k) = T(n-1,k) + T(n-1,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = T(2,1) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Feb 12 2014

Extensions

More terms from Philippe Deléham, Feb 12 2014