A209330 Triangle defined by T(n,k) = binomial(n^2, n*k), for n>=0, k=0..n, as read by rows.

1, 1, 1, 1, 6, 1, 1, 84, 84, 1, 1, 1820, 12870, 1820, 1, 1, 53130, 3268760, 3268760, 53130, 1, 1, 1947792, 1251677700, 9075135300, 1251677700, 1947792, 1, 1, 85900584, 675248872536, 39049918716424, 39049918716424, 675248872536, 85900584, 1, 1

Offset: 0

Author

Paul D. Hanna, Mar 06 2012

Keywords

• nonn
• tabl

Comments

Column 1 equals A014062.

Row sums equal A167009.

Antidiagonal sums equal A209331.

Ignoring initial row T(0,0), equals the logarithmic derivative of the g.f. of triangle A209196.

Examples

			The triangle of coefficients C(n^2,n*k), n>=k, k=0..n, begins:
1;
1, 1;
1, 6, 1;
1, 84, 84, 1;
1, 1820, 12870, 1820, 1;
1, 53130, 3268760, 3268760, 53130, 1;
1, 1947792, 1251677700, 9075135300, 1251677700, 1947792, 1;
1, 85900584, 675248872536, 39049918716424, 39049918716424, 675248872536, 85900584, 1; ...
		

Links

• Paul D. Hanna, Rows n = 0..30, as a flattened table of n, a(n) for n = 0..495

Crossrefs

Cf. A014062 (column 1), A167009 (row sums), A209331, A209196.

Cf. related triangles: A209196 (exp), A228836, A228832, A226234.

Cf. A206830.

Programs

Mathematica

Table[Binomial[n^2, n*k], {n,0,10}, {k,0,n}]//Flatten (* G. C. Greubel, Jan 05 2018 *)

PARI

{T(n,k)=binomial(n^2,n*k)}
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))