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.

1, 2, -4, 1, -4, 4, 2, -11, 19, -4, 12, -82, 142, -84, 4, 288, -2208, 4142, -2262, 422, -4, 34560, -277056, 566448, -327528, 49938, -2504, 4, 24883200, -202141440, 427397472, -267303264, 44330580, -1580666, 17368, -4, 125411328000, -1021977907200, 2179398320640, -1397599077312

Offset: 1

Author

Roger L. Bagula, Feb 04 2008

Keywords

• uned
• sign
• tabl

Comments

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

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

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

Examples

			{1},
{2, -4},
{1, -4, 4},
{2, -11, 19, -4},
{12, -82, 142, -84, 4},
{288, -2208, 4142, -2262, 422, -4},
{34560, -277056, 566448, -327528, 49938, -2504, 4},
{24883200, -202141440, 427397472, -267303264, 44330580, -1580666, 17368, -4},
		

Links

• E. F. Cornelius Jr. and Phill Schultz, Sequences Generated by Polynomials, The American Mathematical Monthly, Vol. 115, No. 2 (Feb., 2008), pp. 154-158.

Crossrefs

Cf. A129862.