Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Nov 20 2018 16:30:45
%S 1,1,-2,1,0,1,3,-3,1,0,-2,1,-4,2,4,-4,1,0,0,1,0,4,0,-4,1,0,0,3,-3,1,5,
%T -5,-5,5,5,-5,1,0,0,0,-2,1,-6,6,6,3,-2,-6,-12,9,6,-6,1,0,-4,0,2,4,-4,
%U 1,0,0,-6,6,3,-5,1,0,0,0,0,1,7,-7,-7,-7,14,7,7
%N Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in p(u), where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.
%C Row n has length A000041(A056239(n)).
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e Triangle begins:
%e 1
%e 1
%e -2 1
%e 0 1
%e 3 -3 1
%e 0 -2 1
%e -4 2 4 -4 1
%e 0 0 1
%e 0 4 0 -4 1
%e 0 0 3 -3 1
%e 5 -5 -5 5 5 -5 1
%e 0 0 0 -2 1
%e -6 6 6 3 -2 -6 -12 9 6 -6 1
%e 0 -4 0 2 4 -4 1
%e 0 0 -6 6 3 -5 1
%e 0 0 0 0 1
%e 7 -7 -7 -7 14 7 7 7 -7 -7 -21 14 7 -7 1
%e 0 0 0 4 0 -4 1
%e For example, row 15 gives: p(32) = -6e(32) + 6e(221) + 3e(311) - 5e(2111) + e(11111).
%Y Row sums are A321753.
%Y Cf. A005651, A008480, A056239, A124794, A124795, A135278, A296150, A319193, A319225, A319226, A321742-A321765, A321854.
%K sign,tabf
%O 1,3
%A _Gus Wiseman_, Nov 20 2018