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

0,6

Links

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

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.

Example

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, ...

Crossrefs

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

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

Cf. A294609, A294758, A294808.

Sequence in context: A171435 A144183 A050153 * A294609 A204180 A319729

Adjacent sequences: A294947 A294948 A294949 * A294951 A294952 A294953

Keyword

nonn,tabl

Author

Seiichi Manyama, Nov 12 2017

Status

approved