A294950 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j^(k*j)*x^j)^j in powers of x.

1, 1, 1, 1, 1, 3, 1, 1, 9, 6, 1, 1, 33, 90, 13, 1, 1, 129, 2220, 1162, 24, 1, 1, 513, 59178, 265132, 17435, 48, 1, 1, 2049, 1594836, 67180330, 49163241, 310193, 86, 1, 1, 8193, 43048770, 17181660628, 152662629227, 13121450895, 6286826, 160

Offset: 0

Author

Seiichi Manyama, Nov 12 2017

Keywords

• nonn
• tabl

Examples

			Square array begins:
    1,     1,        1,            1,               1, ...
    1,     1,        1,            1,               1, ...
    3,     9,       33,          129,             513, ...
    6,    90,     2220,        59178,         1594836, ...
   13,  1162,   265132,     67180330,     17181660628, ...
   24, 17435, 49163241, 152662629227, 476855156157129, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..52, flattened

Crossrefs

Columns k=0..2 give A000219, A294813, A294954.

Rows n=0+1, 2 give A000012, A087289.

Cf. A294609, A294758, A294808.

Formula

A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j)) * A(n-j,k) for n > 0.