login
A294756
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(k*j) in powers of x.
3
1, 1, 1, 1, 1, 2, 1, 1, 17, 3, 1, 1, 257, 746, 5, 1, 1, 4097, 531698, 66442, 7, 1, 1, 65537, 387424586, 4295533810, 9843731, 11, 1, 1, 1048577, 282429602018, 281475372654922, 95371863223331, 2187951485, 15, 1, 1, 16777217, 205891133143226, 18446744358295025890, 931322857677725493491, 4738477951108288824, 680615166718, 22
OFFSET
0,6
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*(d+j))) * A(n-j,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, ...
1, 1, 1, 1, ...
2, 17, 257, 4097, ...
3, 746, 531698, 387424586, ...
5, 66442, 4295533810, 281475372654922, ...
CROSSREFS
Columns k=0..1 give A000041, A294757.
Rows n=0-1 give A000012.
Cf. A294699.
Sequence in context: A173504 A322621 A309036 * A174918 A154991 A090163
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Nov 08 2017
STATUS
approved