A126682 Square pyramid giving coefficients of Carlo Wood's polynomials, read by successive slices, each slice being read row by row.

1, 1, 1, 1, 3, 1, 3, 2, 2, 9, 7, 1, 6, 11, 1, 6, 11, 6, 3, 22, 45, 26, 3, 26, 69, 46, 1, 10, 35, 50, 1, 10, 35, 50, 24, 4, 45, 170, 255, 126, 6, 75, 320, 525, 274, 4, 55, 270, 545, 326, 1, 15, 85, 225, 274, 1, 15, 85, 225, 274, 120, 5, 81, 485, 1335, 1670, 744, 10

Offset: 1

Author

N. J. A. Sloane, Feb 14 2007

Keywords

• nonn
• tabf

Comments

There is no standard method for converting a pyramid of numbers to a sequence. This seems as good a solution as any.

See the link for further information and more terms.

The first row of each slice seems to coincide with the first row of each slice of A335442. That row from the n-th slice seems to be the coefficients of the polynomial (x+1) * ... * (x+n-1), i.e., the reversed row n-1 of A130534. - Andrey Zabolotskiy, Jun 26 2022

Examples

			Slice 1:
  1
Slice 2:
  1 1
  1 3
Slice 3:
  1  3  2
  2  9  7
  1  6 11
Slice 4:
  1  6 11  6
  3 22 45 26
  3 26 69 46
  1 10 35 50
Note that in Part 4 of the linked file, the order of the rows is reversed, while in its Part 1 the order of both rows and columns is reversed.
		

Links

• N. J. A. Sloane, Notes on Carlo Wood's Polynomials

Crossrefs

Cf. A126671, A130534, A335442.

Extensions

The sole term 1 of slice 1 inserted by Andrey Zabolotskiy, Jun 26 2022