A117178 -id:A117178 - cp's OEIS frontend

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

Mohammad K. Azarian

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

			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;

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

Cf. A014413, A034868, A058622 (row sums).
Cf. A001791 (a half-diagonal and diagonal sums).
Cf. A007318, A000037, A008314.
Cf. A117178.

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

More terms from James Sellers

A117179 Riordan array ((1-x^2)/(1+x^2)^2,x/(1+x^2)).

Original entry on oeis.org

1, 0, 1, -3, 0, 1, 0, -4, 0, 1, 5, 0, -5, 0, 1, 0, 9, 0, -6, 0, 1, -7, 0, 14, 0, -7, 0, 1, 0, -16, 0, 20, 0, -8, 0, 1, 9, 0, -30, 0, 27, 0, -9, 0, 1, 0, 25, 0, -50, 0, 35, 0, -10, 0, 1, -11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1

Offset: 0

Paul Barry, Mar 01 2006

Inverse is A117178. Row sums are (-1)^n*A098554(n+1). Diagonal sums are 1,0,-2,0,2,0,-2,... with g.f. (1-x^2)/(1+x^2).

Apparently, with the rows de-aerated and then reversed, this matrix becomes signed A034807 with the twos on the diagonal removed. Apparently, |D(2n,k+1)| = |D(2(n-1),k+1)| + |D(2n,k)| where D(n,k) is the k-th element on the n-th diagonal. - Tom Copeland, May 30 2017

			Triangle begins
1,
0, 1,
-3, 0, 1,
0, -4, 0, 1,
5, 0, -5, 0, 1,
0, 9, 0, -6, 0, 1,
-7, 0, 14, 0, -7, 0, 1,
0, -16, 0, 20, 0, -8, 0, 1

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Extensions