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A321761
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in s(u), where H is Heinz number, m is monomial symmetric functions, and s is Schur functions.
2
1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 3, 4, 0, 0, 1, 2, 1, 3, 5, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,12
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).
FORMULA
If s(y) = Sum_{|z| = |y|} c(y,z) * m(z), then Sum_{|z| = |y|} c(y,z) * P(z) = A296188(H(y)), where P(y) is the number of distinct permutations of y.
EXAMPLE
Triangle begins:
1
1
1 1
0 1
1 1 1
0 1 2
1 1 1 1 1
0 0 1
0 1 0 1 2
0 1 1 2 3
1 1 1 1 1 1 1
0 0 0 1 3
1 1 1 1 1 1 1 1 1 1 1
0 1 1 2 2 3 4
0 0 1 2 1 3 5
0 0 0 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 1 0 2 5
For example, row 15 gives: s(32) = m(32) + 2m(221) + m(311) + 3m(2111) + 5m(11111).
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved