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A321750 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in p(u), where H is Heinz number, m is monomial symmetric functions, and p is power sum symmetric functions. 9
1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 3, 6, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 6, 4, 12, 24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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).

LINKS

Table of n, a(n) for n=1..86.

Wikipedia, Symmetric polynomial

EXAMPLE

Triangle begins:

   1

   1

   1   0

   1   2

   1   0   0

   1   1   0

   1   0   0   0   0

   1   3   6

   1   2   0   0   0

   1   0   1   0   0

   1   0   0   0   0   0   0

   1   2   2   2   0

   1   0   0   0   0   0   0   0   0   0   0

   1   1   0   0   0   0   0

   1   0   1   0   0   0   0

   1   6   4  12  24

   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0

   1   1   2   2   0   0   0

For example, row 18 gives: p(221) = m(5) + 2m(32) + m(41) + 2m(221).

CROSSREFS

Row sums are A321751.

Cf. A005651, A008277, A008480, A048994, A056239, A124794, A124795, A319182, A319191, A321742-A321765.

Sequence in context: A035227 A328556 A321888 * A345374 A056929 A304096

Adjacent sequences:  A321747 A321748 A321749 * A321751 A321752 A321753

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Nov 20 2018

STATUS

approved

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Last modified January 18 09:26 EST 2022. Contains 350454 sequences. (Running on oeis4.)