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

1,4

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

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

Example

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;

Prog

(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

Crossrefs

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

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

Cf. A007318, A000037, A008314.

Cf. A117178.

Sequence in context: A057466 A187079 A086183 * A309992 A016474 A332678

Adjacent sequences: A014459 A014460 A014461 * A014463 A014464 A014465

Keyword

tabf,nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers

Status

approved