A321916 - OEIS

A321916

Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in h(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and h is homogeneous symmetric functions.

1, -1, 1, 0, 1, 1, -2, 1, 0, -1, 1, 0, 0, 1, -1, 1, 2, -3, 1, 0, 1, 0, -2, 1, 0, 0, 1, -2, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 1, -2, -2, 3, 3, -4, 1, 0, -1, 0, 1, 2, -3, 1, 0, 0, -1, 2, 1, -3, 1, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, -1, 1

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OFFSET

1,7

COMMENTS

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Also the coefficient of h(v) in e(u).

LINKS

Table of n, a(n) for n=1..81.

Wikipedia, Symmetric polynomial

EXAMPLE

Tetrangle begins (zeroes not shown):

(1): 1

(2): -1 1

(11): 1

(3): 1 -2 1

(21): -1 1

(111): 1

(4): -1 1 2 -3 1

(22): 1 -2 1

(31): 1 -2 1

(211): -1 1

(1111): 1

(5): 1 -2 -2 3 3 -4 1

(41): -1 1 2 -3 1

(32): -1 2 1 -3 1

(221): 1 -2 1

(311): 1 -2 1

(2111): -1 1

(11111): 1

For example, row 14 gives: h(32) = -e(32) + 2e(221) + e(311) - 3e(2111) + e(11111).

CROSSREFS

This is a regrouping of the triangle A321749. Row sums are A134286.

Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.

Sequence in context: A016102 A083905 A179319 * A257265 A045706 A045634

Adjacent sequences: A321913 A321914 A321915 * A321917 A321918 A321919

KEYWORD

sign,tabf

AUTHOR

Gus Wiseman, Nov 22 2018

STATUS

approved