A014462 Triangular array formed from elements to left of middle of Pascal's triangle.

1, 1, 1, 3, 1, 4, 1, 5, 10, 1, 6, 15, 1, 7, 21, 35, 1, 8, 28, 56, 1, 9, 36, 84, 126, 1, 10, 45, 120, 210, 1, 11, 55, 165, 330, 462, 1, 12, 66, 220, 495, 792, 1, 13, 78, 286, 715, 1287, 1716, 1, 14, 91, 364, 1001, 2002, 3003, 1, 15, 105, 455, 1365, 3003, 5005, 6435, 1, 16

Offset: 1

Author

Mohammad K. Azarian

Keywords

• tabf
• nonn
• easy

Comments

Coefficients for Pontryagin classes of projective spaces. See p. 3 of the Wilson link. Aerated to become a lower triangular matrix with alternating zeros on the diagonal, this matrix appparently becomes the reverse, or mirror, of A117178. - Tom Copeland, May 30 2017

Examples

			Array begins:
  1;
  1;
  1,  3;
  1,  4;
  1,  5, 10;
  1,  6, 15;
  1,  7, 21,  35;
  1,  8, 28,  56;
  1,  9, 36,  84, 126;
  1, 10, 45, 120, 210;
  1, 11, 55, 165, 330, 462;
		

Links

• Reinhard Zumkeller, Rows n = 1..200 of triangle, flattened
• Jon Maiga, Computer-generated formulas for A014462, Sequence Machine.
• D. Wilson, Genera: From cobordism to K-theory, Jul 2016.
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A014413, A034868, A058622 (row sums).

Cf. A001791 (a half-diagonal and diagonal sums).

Cf. A007318, A000037, A008314.

Cf. A117178.

Programs

Haskell

a014462 n k = a014462_tabf !! (n-1) !! (k-1)
a014462_row n = a014462_tabf !! (n-1)
a014462_tabf = map reverse a014413_tabf
-- Reinhard Zumkeller, Dec 24 2015

Extensions

More terms from James Sellers