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A321888 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of f(v) in p(u), where H is Heinz number, p is power sum symmetric functions, and f is forgotten symmetric functions. 2
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 (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).

Up to sign, a(n) is also the coefficient of m(v) in p(u), where m is monomial symmetric functions.

LINKS

Table of n, a(n) for n=1..82.

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 12 gives: p(211) = -f(4) - 2f(22) - 2f(31) - 2f(211).

CROSSREFS

Row sums are A321889.

Cf. A005651, A008277, A008480, A048994, A056239, A124794, A124795, A319182, A319193, A321742-A321765.

Sequence in context: A035227 A049340 A328556 * A321750 A056929 A304096

Adjacent sequences:  A321885 A321886 A321887 * A321889 A321890 A321891

KEYWORD

sign,tabf

AUTHOR

Gus Wiseman, Nov 20 2018

STATUS

approved

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Last modified May 28 03:04 EDT 2020. Contains 334671 sequences. (Running on oeis4.)