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Revision History for A288199 (Underlined text is an addition; strikethrough text is a deletion.)

Showing entries 1-10 | older changes
A288199 Irregular triangle read by rows: mean version of Girard-Waring formula (cf. A210258), for m = 4 data values.
(history; published version)
#32 by N. J. A. Sloane at Tue Jul 04 09:28:25 EDT 2017
STATUS

reviewed

approved

#31 by Michel Marcus at Tue Jul 04 00:57:28 EDT 2017
STATUS

proposed

reviewed

#30 by Jon E. Schoenfield at Tue Jul 04 00:42:50 EDT 2017
STATUS

editing

proposed

#29 by Jon E. Schoenfield at Tue Jul 04 00:42:46 EDT 2017
COMMENTS

Let SM_k = Sum( d_(t_1, t_2, t_3, t_4)* eM_1^t_1 * eM_2^t_2 * eM_3^t_3*eM_4^t_4) summed over all length 4 integer partitions of k, i.e., 1*t_1+ + 2*t_2+ + 3*t_3+ + 4*t_4= = k, where SM_k are the averaged k-th power sum symmetric polynomials in 4 data (i.e., SM_k = S_k/4 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(4,k) with e_k being the k-th elementary symmetric polynomials. The data d_(t_1, t_2, t_3, t_4) form an irregular triangle, with one row for each k value starting with k=1; "irregular" means that the number of terms in successive rows is nondecreasing.

STATUS

proposed

editing

#28 by Gregory Gerard Wojnar at Mon Jul 03 23:11:21 EDT 2017
STATUS

editing

proposed

#27 by Gregory Gerard Wojnar at Mon Jul 03 23:10:47 EDT 2017
CROSSREFS

Cf. A210258., A028297 (m=2), A287768 (m=3), A288207 (m=5), A288211 (m=6), A288245 (m=7), A288188 (m=8).

STATUS

approved

editing

Discussion
Mon Jul 03 23:11
Gregory Gerard Wojnar: Added cross-refs
#26 by Alois P. Heinz at Thu Jun 29 16:39:27 EDT 2017
STATUS

proposed

approved

#25 by Wesley Ivan Hurt at Thu Jun 29 14:35:59 EDT 2017
STATUS

editing

proposed

#24 by Wesley Ivan Hurt at Thu Jun 29 14:35:44 EDT 2017
CROSSREFS

Cf. A210258.

STATUS

proposed

editing

#23 by Michel Marcus at Thu Jun 29 10:44:07 EDT 2017
STATUS

editing

proposed

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Last modified September 1 03:07 EDT 2024. Contains 375575 sequences. (Running on oeis4.)