

A059674


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


2



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
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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[mn, n], {m, 0, 12}, {n, 0, m}] // Flatten (* JeanFrançois Alcover, Oct 10 2012 *)


CROSSREFS

Cf. A007318.
Sequence in context: A319989 A184305 A157522 * A117545 A047000 A288915
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



