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 A321896 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in e(u) * Product_i u_i!, where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions. 2
 1, 1, -1, 1, 0, 1, 2, -3, 1, 0, -1, 1, -6, 3, 8, -6, 1, 0, 0, 1, 0, 1, 0, -2, 1, 0, 0, 2, -3, 1, 24, -30, -20, 15, 20, -10, 1, 0, 0, 0, -1, 1, -120, 90, 144, 40, -15, -90, -120, 45, 40, -15, 1, 0, -6, 0, 3, 8, -6, 1, 0, 0, -2, 3, 2, -4, 1, 0, 0, 0, 0, 1, 720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 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..73. Wikipedia, Symmetric polynomial EXAMPLE Triangle begins: 1 1 -1 1 0 1 2 -3 1 0 -1 1 -6 3 8 -6 1 0 0 1 0 1 0 -2 1 0 0 2 -3 1 24 -30 -20 15 20 -10 1 0 0 0 -1 1 -120 90 144 40 -15 -90 -120 45 40 -15 1 0 -6 0 3 8 -6 1 0 0 -2 3 2 -4 1 0 0 0 0 1 720 -840 -504 -420 630 504 210 280 -105 -210 -420 105 70 -21 1 0 0 0 1 0 -2 1 For example, row 15 gives: 12e(32) = -2p(32) + 3p(221) + 2p(311) - 4p(2111) + p(11111). CROSSREFS Row sums are A036987. Cf. A005651, A008480, A056239, A124794, A124795, A135278, A319193, A319225, A319226, A321742-A321765, A321897. Sequence in context: A030373 A079343 A004566 * A321897 A050074 A346688 Adjacent sequences: A321893 A321894 A321895 * A321897 A321898 A321899 KEYWORD sign,tabf AUTHOR Gus Wiseman, Nov 20 2018 STATUS approved

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Last modified September 10 19:41 EDT 2024. Contains 375794 sequences. (Running on oeis4.)