A294296 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Sum_{j>=1} sigma_k(j) * x^j).

1, 1, 1, 1, 1, 5, 1, 1, 7, 25, 1, 1, 11, 43, 193, 1, 1, 19, 91, 409, 1481, 1, 1, 35, 223, 1105, 3841, 16021, 1, 1, 67, 595, 3505, 13841, 50431, 167665, 1, 1, 131, 1663, 12193, 60841, 230731, 648187, 2220065, 1, 1, 259, 4771, 44689, 297761, 1340851, 3955771

Offset: 0

Author

Seiichi Manyama, Oct 30 2017

Keywords

• nonn
• tabl

Examples

			Square array A(n,k) begins:
      1,    1,     1,     1,      1, ...
      1,    1,     1,     1,      1, ...
      5,    7,    11,    19,     35, ...
     25,   43,    91,   223,    595, ...
    193,  409,  1105,  3505,  12193, ...
   1481, 3841, 13841, 60841, 297761, ...
		

Links

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

Crossrefs

Columns k=0..2 give A294363, A294361, A294362.

Rows n=0-1 give A000012.

Main diagonal gives A294388.

Cf. A144048.

Formula

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