OFFSET
1,2
COMMENTS
Let SM_k = Sum( d_(t_1, t_2, t_3, ..., t_8)* eM_1^t_1 * eM_2^t_2 * ...*eM_8^t_8) summed over all length 8 integer partitions of k, i.e., 1*t_1+2*t_2+3*t_3+...+8*t_8=k, where SM_k are the averaged k-th power sum symmetric polynomials in 8 data (i.e., SM_k = S_k/8 where S_k are the k-th power sum symmetric polynomials, and where eM_k are the averaged k-th elementary symmetric polynomials, eM_k = e_k/binomial(8,k) with e_k being the k-th elementary symmetric polynomials. The data d_(t_1, t_2, t_3, ..., t_8) form a triangle, with one row for each k value starting with k=1; the number of terms in successive rows is nondecreasing.
Row sums of positive entries give: 1,8,85,932,10291,114878,... Row sums of negative entries are always 1 less than corresponding row sums of positive entries.
LINKS
Gregory Gerard Wojnar, Java program
G. G. Wojnar, D. Sz. Wojnar, and L. Q. Brin, Universal Peculiar Linear Mean Relationships in All Polynomials, pp. 22-24, arXiv:1706.08381 [math.GM], 2017.
EXAMPLE
Triangle begins
1;
8, -7;
64, -84, 21;
512, -896, 224, 196, -35;
4096, -8960, 2240, 3920, -350, -980, 35;
...
PROG
(Java) See link.
CROSSREFS
KEYWORD
sign,tabf
AUTHOR
Gregory Gerard Wojnar, Jun 16 2017
STATUS
approved