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

0,8

Links

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

Formula

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

Example

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 ...

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 *)

Crossrefs

Cf. A007318.

Sequence in context: A184305 A337279 A157522 * A367624 A342748 A117545

Adjacent sequences: A059671 A059672 A059673 * A059675 A059676 A059677

Keyword

easy,nice,nonn,tabl

Author

Fabian Rothelius, Feb 05 2001

Extensions

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

Status

approved