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A symmetrical triangle of adjusted polynomial coefficients based on Hermite orthogonal polynomials.
2

%I #5 Apr 27 2019 05:24:58

%S 1,1,1,1,9,1,1,1,1,1,1,-191,2113,-191,1,1,1,1,1,1,1,1,7681,-337919,

%T 7681,-337919,7681,1,1,1,1,1,1,1,1,1,1,-430079,47738881,-430079,

%U 180203521,-430079,47738881,-430079,1,1,1,1,1,1,1,1,1,1,1

%N A symmetrical triangle of adjusted polynomial coefficients based on Hermite orthogonal polynomials.

%C Row sums are: {1, 2, 11, 4, 1733, 6, -652793, 8, 273960969, 10, -143712092149, ...}.

%H G. C. Greubel, <a href="/A176410/b176410.txt">Rows n = 0..50 of triangle, flattened</a>

%e Triangle begins as:

%e 1;

%e 1, 1;

%e 1, 9, 1;

%e 1, 1, 1, 1;

%e 1, -191, 2113, -191, 1;

%e 1, 1, 1, 1, 1, 1;

%e 1, 7681, -337919, 7681, -337919, 7681, 1;

%e 1, 1, 1, 1, 1, 1, 1, 1;

%t 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;

%t Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten

%Y Cf. A060821.

%K less,sign,tabl

%O 0,5

%A _Roger L. Bagula_, Apr 16 2010

%E Edited by _G. C. Greubel_, Apr 26 2019