A294946 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of exp(Sum_{j>0} sigma_k(j)*x^j/j) in powers of x.

1, 1, 1, 1, 1, 3, 1, 1, 5, 12, 1, 1, 9, 32, 82, 1, 1, 17, 90, 304, 725, 1, 1, 33, 260, 1162, 3537, 8811, 1, 1, 65, 762, 4516, 17435, 52010, 128340, 1, 1, 129, 2252, 17722, 86529, 310193, 895397, 2257687, 1, 1, 257, 6690, 69964, 431675, 1865766, 6286826, 18016416, 45658174

Offset

0,6

Links

Table of n, a(n) for n=0..54.

Formula

G.f. of column k: Product_{j>0} 1/(1 - j^j*x^j)^(j^(k-1)).

Example

Square array begins:
     1,    1,     1,     1,      1, ...
     1,    1,     1,     1,      1, ...
     3,    5,     9,    17,     33, ...
    12,   32,    90,   260,    762, ...
    82,  304,  1162,  4516,  17722, ...
   725, 3537, 17435, 86529, 431675, ...

Crossrefs

Columns k=0..2 give A023881, A023882, A294813.

Rows n=0+1, 2 give A000012, A000051(n+1).

Cf. A294296, A294947.

Sequence in context: A123162 A213998 A340970 * A083075 A335333 A341470

Adjacent sequences: A294943 A294944 A294945 * A294947 A294948 A294949

Keyword

nonn,tabl

Author

Seiichi Manyama, Nov 11 2017

Status

approved