A321747 - OEIS

A321747

Sum of coefficients of elementary symmetric functions in the monomial symmetric function of the integer partition with Heinz number n.

1, 1, -1, 1, 1, -2, -1, 1, 1, 2, 1, -3, -1, -2, -2, 1, 1, 3, -1, 3, 2, 2, 1, -4, 1, -2, -1, -3, -1, -6, 1, 1, -2, 2, -2, 6, -1, -2, 2, 4, 1, 6, -1, 3, 3, 2, 1, -5, 1, 3, -2, -3, -1, -4, 2, -4, 2, -2, 1, -12, -1, 2, -3, 1, -2, -6, 1, 3, -2, -6, -1, 10, 1, -2

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OFFSET

1,6

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..74.

Wikipedia, Symmetric polynomial

FORMULA

a(n) = (-1)^(A056239(n) - A001222(n)) * A008480(n).

EXAMPLE

The sum of coefficients of m(2211) = 9e(6) + e(42) - 4e(51) is a(36) = 6.