A059674 Square array a(m,n) = binomial(max(m,n), min(m,n)) (m>=0, n>=0) read by antidiagonals.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 1, 3, 1, 1, 4, 3, 3, 4, 1, 1, 5, 6, 1, 6, 5, 1, 1, 6, 10, 4, 4, 10, 6, 1, 1, 7, 15, 10, 1, 10, 15, 7, 1, 1, 8, 21, 20, 5, 5, 20, 21, 8, 1, 1, 9, 28, 35, 15, 1, 15, 35, 28, 9, 1, 1, 10, 36, 56, 35, 6, 6, 35, 56, 36, 10, 1, 1, 11, 45, 84, 70, 21, 1, 21, 70, 84

Offset: 0

Author

Fabian Rothelius, Feb 05 2001

Keywords

• easy
• nice
• nonn
• tabl

Examples

			a(2,4) = binomial(max(2,4), min(2,4)) = binomial(4,2) = 6.
Square begins:
1 1 1 1 1 1 ...
1 1 2 3 4 5 ...
1 2 1 3 6 10...
1 3 3 1 4 10 ...
		

Links

• T. D. Noe, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A007318.

Programs

Mathematica

a[m_, n_] := If[m >= n, Binomial[m, n], Binomial[n, m]]; Table[a[m-n, n], {m, 0, 12}, {n, 0, m}] // Flatten (* Jean-François Alcover, Oct 10 2012 *)

Formula

Square array equals A007318 + transpose(A007318) - I, where I denotes the infinite identity matrix. - Peter Bala, Aug 11 2015

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Feb 06 2001