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A321894 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in f(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions. 1
1, 1, -1, 1, 1, 0, 1, -1, 1, -2, 1, 0, -1, 0, 1, -1, 1, 1, 0, 0, 1, 1, -1, 0, 0, 2, -1, -1, 1, 0, 1, -1, 0, 0, 1, -1, 1, -3, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, -1, 1, -2, 1, 1, -1, -1, 1, 0, -2, 2, -1, 1, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

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..67.

Wikipedia, Symmetric polynomial

EXAMPLE

Triangle begins:

   1

   1

  -1   1

   1   0

   1  -1   1

  -2   1   0

  -1   0   1  -1   1

   1   0   0

   1   1  -1   0   0

   2  -1  -1   1   0

   1  -1   0   0   1  -1   1

  -3   0   1   0   0

  -1   0   1   0   0  -1   0   0   1  -1   1

  -2   1   1  -1  -1   1   0

  -2   2  -1   1  -1   0   0

For example, row 15 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).

CROSSREFS

Row sums are A321764.

Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A317552, A321742-A321765, A321892.

Sequence in context: A037889 A339872 A280269 * A330262 A098055 A344739

Adjacent sequences:  A321891 A321892 A321893 * A321895 A321896 A321897

KEYWORD

sign,tabf,more

AUTHOR

Gus Wiseman, Nov 20 2018

STATUS

approved

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Last modified June 18 11:55 EDT 2021. Contains 345098 sequences. (Running on oeis4.)