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A321897
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in h(u) * Product_i u_i!, where H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions.
3
1, 1, 1, 1, 0, 1, 2, 3, 1, 0, 1, 1, 6, 3, 8, 6, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 3, 1, 24, 30, 20, 15, 20, 10, 1, 0, 0, 0, 1, 1, 120, 90, 144, 40, 15, 90, 120, 45, 40, 15, 1, 0, 6, 0, 3, 8, 6, 1, 0, 0, 2, 3, 2, 4, 1, 0, 0, 0, 0, 1, 720, 840, 504, 420, 630
OFFSET
1,7
COMMENTS
Row n has length A000041(A056239(n)).
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Triangle begins:
1
1
1 1
0 1
2 3 1
0 1 1
6 3 8 6 1
0 0 1
0 1 0 2 1
0 0 2 3 1
24 30 20 15 20 10 1
0 0 0 1 1
120 90 144 40 15 90 120 45 40 15 1
0 6 0 3 8 6 1
0 0 2 3 2 4 1
0 0 0 0 1
720 840 504 420 630 504 210 280 105 210 420 105 70 21 1
0 0 0 1 0 2 1
For example, row 14 gives: 12h(41) = 6p(41) + 3p(221) + 8p(311) + 6p(2111) + p(11111).
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved