A175011 Triangle read by rows, antidiagonals of an array generated from INVERT transforms of variants of (1, 2, 3, ...).

1, 1, 2, 1, 2, 5, 1, 2, 2, 16, 1, 2, 2, 5, 45, 1, 2, 2, 2, 12, 125, 1, 2, 2, 2, 5, 24, 341, 1, 2, 2, 2, 2, 12, 48, 918, 1, 2, 2, 2, 2, 7, 18, 97, 2453, 1, 2, 2, 2, 2, 2, 16, 28, 195, 6515

Offset: 1

Author

Gary W. Adamson, Apr 03 2010

Keywords

• nonn
• tabl

Comments

Row sums = A001906, the even-indexed Fibonacci numbers starting (1, 3, 8, 21, ...).

Examples

			First few rows of the array:
  1, 3, 8, 21, 55, 144, 377, 987, 2584, ...
  1, 1, 3,  5, 10,  19,  36,  69,  131, ...
  1, 1, 1,  3,  5,   7,  12,  21,   34, ...
  1, 1, 1,  1,  3,   5,   7,   9,   16, ...
  1, 1, 1,  1,  1,   3,   5,   7,    9, ...
  1, 1, 1,  1,  1,   1,   3,   5,    7, ...
  ...
Taking finite differences from the bottom to top starting with the last "1" we obtain triangle A175011:
  1;
  1, 2;
  1, 2, 5;
  1, 2, 2, 16;
  1, 2, 2,  5, 45;
  1, 2, 2,  2, 12, 125;
  1, 2, 2,  2,  5,  24, 341;
  1, 2, 2,  2,  2,  12,  48, 918;
  1, 2, 2,  2,  2,   7,  18,  97, 2453;
  1, 2, 2,  2,  2,   2,  16,  28,  195, 6515;
  ...
		

Crossrefs

Cf. A001906.

Formula

Given S(x) = (1 + 2x + 3x^2 + ...), where (1, 2, 3, ...) = the INVERTi transform of (1, 3, 8, 21, 55, ...); k-th row of the array = INVERT transform of S(x^k). Take finite differences of array columns starting from the topmost "1"; becoming rows of the triangle.