A321753 Sum of coefficients of elementary symmetric functions in the power sum symmetric function indexed by the integer partition with Heinz number n.

1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1

Offset

1

Comments

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..60.

Wikipedia, Symmetric polynomial

Formula

a(n) = 1 if n is the Heinz number of an integer partition with an even number of even parts, otherwise a(n) = -1.

Example

The sum of coefficients of p(32) = -6e(32) + 6e(221) + 3e(311) - 5e(2111) + e(11111) is a(15) = -1.

Crossrefs

Row sums of A321752.

Cf. A005651, A008480, A056239, A124794, A124795, A135278, A296150, A319193, A319225, A319226, A321742-A321765.

Sequence in context: A016030 A123271 A121238 * A186032 A212157 A131554

Adjacent sequences: A321750 A321751 A321752 * A321754 A321755 A321756

Keyword

sign,more

Author

Gus Wiseman, Nov 20 2018

Status

approved