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A176410
A symmetrical triangle of adjusted polynomial coefficients based on Hermite orthogonal polynomials.
2
1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, -191, 2113, -191, 1, 1, 1, 1, 1, 1, 1, 1, 7681, -337919, 7681, -337919, 7681, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -430079, 47738881, -430079, 180203521, -430079, 47738881, -430079, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
0,5
COMMENTS
Row sums are: {1, 2, 11, 4, 1733, 6, -652793, 8, 273960969, 10, -143712092149, ...}.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 9, 1;
1, 1, 1, 1;
1, -191, 2113, -191, 1;
1, 1, 1, 1, 1, 1;
1, 7681, -337919, 7681, -337919, 7681, 1;
1, 1, 1, 1, 1, 1, 1, 1;
MATHEMATICA
T[n_, m_]:= CoefficientList[HermiteH[n, x], x][[m + 1]]Reverse[ CoefficientList[ HermiteH[n, x], x]][[m + 1]] - (CoefficientList[ HermiteH[n, x], x][[1]]Reverse[CoefficientList[HermiteH[n, x], x]][[1]]) + 1;
Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten
CROSSREFS
Cf. A060821.
Sequence in context: A113061 A366904 A284099 * A087966 A087968 A340365
KEYWORD
less,sign,tabl
AUTHOR
Roger L. Bagula, Apr 16 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 26 2019
STATUS
approved