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A135185 Triangle read by rows: E. F. Cornelius Jr. and Phill Schultz-based polynomials for the D_n Cartan Matrices in sequence A129862 that give a triangular sequence. 0

%I #11 Feb 08 2015 07:02:46

%S 1,2,-4,1,-4,4,2,-11,19,-4,12,-82,142,-84,4,288,-2208,4142,-2262,422,

%T -4,34560,-277056,566448,-327528,49938,-2504,4,24883200,-202141440,

%U 427397472,-267303264,44330580,-1580666,17368,-4,125411328000,-1021977907200,2179398320640,-1397599077312

%N Triangle read by rows: E. F. Cornelius Jr. and Phill Schultz-based polynomials for the D_n Cartan Matrices in sequence A129862 that give a triangular sequence.

%C These polynomials are suggested by Corollary 2.4 in the E. F. Cornelius Jr. and Phill Schultz paper.

%C It appears that many other fundamental matrix sequences can be related to these Cornelius-Schultz polynomials by a similar treatment.

%C Here a factor of 4 was necessary to convert them all to integer form.

%H E. F. Cornelius Jr. and Phill Schultz, <a href="http://www.jstor.org/stable/27642423">Sequences Generated by Polynomials</a>, The American Mathematical Monthly, Vol. 115, No. 2 (Feb., 2008), pp. 154-158.

%e {1},

%e {2, -4},

%e {1, -4, 4},

%e {2, -11, 19, -4},

%e {12, -82, 142, -84, 4},

%e {288, -2208, 4142, -2262, 422, -4},

%e {34560, -277056, 566448, -327528, 49938, -2504, 4},

%e {24883200, -202141440, 427397472, -267303264, 44330580, -1580666, 17368, -4},

%Y Cf. A129862.

%K uned,sign,tabl

%O 1,2

%A _Roger L. Bagula_, Feb 04 2008

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Last modified April 23 22:36 EDT 2024. Contains 371917 sequences. (Running on oeis4.)