OFFSET
0,61
FORMULA
T(n,k) is the coefficient of x^n * y^k in the expansion of Product_{i > 0} 1/(1 - y * x^(i!)).
EXAMPLE
Triangle begins:
1
0 1
0 1 1
0 0 1 1
0 0 1 1 1
0 0 0 1 1 1
0 1 0 1 1 1 1
0 0 1 0 1 1 1 1
0 0 1 1 1 1 1 1 1
0 0 0 1 1 1 1 1 1 1
0 0 0 1 1 2 1 1 1 1 1
0 0 0 0 1 1 2 1 1 1 1 1
0 0 1 0 1 1 2 2 1 1 1 1 1
0 0 0 1 0 1 1 2 2 1 1 1 1 1
0 0 0 1 1 1 1 2 2 2 1 1 1 1 1
0 0 0 0 1 1 1 1 2 2 2 1 1 1 1 1
0 0 0 0 1 1 2 1 2 2 2 2 1 1 1 1 1
0 0 0 0 0 1 1 2 1 2 2 2 2 1 1 1 1 1
0 0 0 1 0 1 1 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 1 0 1 1 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 1 1 1 1 2 2 3 2 2 2 2 2 1 1 1 1 1
Row n = 12 counts the following partitions:
(66)
(6222)
(62211)
(222222) (621111)
(2222211) (6111111)
(22221111)
(222111111)
(2211111111)
(21111111111)
(111111111111)
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1-y*x^(i!)), {i, 1, n}], {x, 0, n}, {y, 0, k}], {n, 0, 15}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, May 12 2019
STATUS
approved