A294118 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(k*((1+x)^k - 1)).

1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 9, 20, 1, 0, 1, 16, 99, 112, 1, 0, 1, 25, 304, 1233, 688, 1, 0, 1, 36, 725, 6496, 16929, 4544, 1, 0, 1, 49, 1476, 23425, 152416, 251829, 31936, 1, 0, 1, 64, 2695, 66816, 826225, 3867136, 4012011, 236800, 1, 0, 1, 81, 4544, 162337

Offset: 0

Author

Seiichi Manyama, Oct 23 2017

Keywords

• nonn
• tabl

Examples

			Square array A(n,k) begins:
   1, 1,    1,      1,       1, ...
   0, 1,    4,      9,      16, ...
   0, 1,   20,     99,     304, ...
   0, 1,  112,   1233,    6496, ...
   0, 1,  688,  16929,  152416, ...
   0, 1, 4544, 251829, 3867136, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened

Crossrefs

Columns k=0..3 give A000007, A000012, A294119, A294120.

Rows n=0..1 give A000012, A000290.

Main diagonal gives A294191.

Cf. A293991, A294042.

Formula

A(0,k) = 1 and A(n,k) = k^2 * (n-1)! * Sum_{j=1..min(k,n)} binomial(k-1,j-1)*A(n-j,k)/(n-j)! for n > 0.