A176411 - OEIS

%I #2 Mar 30 2012 17:34:40

%S 1,1,1,1,-1,1,1,-19,-19,1,1,-27,-123,-27,1,1,89,-191,-191,89,1,1,57,

%T 297,57,297,57,1,1,-1807,-1471,3233,3233,-1471,-1807,1,1,-1935,-18959,

%U -1935,24945,-1935,-18959,-1935,1,1,29729,-9727,-81151,47873,47873,-81151

%N A symmetrical triangle of leading ones adjusted polynomial coefficients based on Hermite orthogonal polynomials: 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

%C Row sums are:

%C {1, 2, 1, -36, -175, -202, 767, -88, -20711, -26550, 337835,...}.

%C Sequence A176410 was discovered by a typing mistake;

%C I left out the plus signs and Mathematica made it multiplication instead.

%F 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

%e {1},

%e {1, 1},

%e {1, -1, 1},

%e {1, -19, -19, 1},

%e {1, -27, -123, -27, 1},

%e {1, 89, -191, -191, 89, 1},

%e {1, 57, 297, 57, 297, 57, 1},

%e {1, -1807, -1471, 3233, 3233, -1471, -1807, 1},

%e {1, -1935, -18959, -1935, 24945, -1935, -18959, -1935, 1},

%e {1, 29729, -9727, -81151, 47873, 47873, -81151, -9727, 29729, 1},

%e {1, 29217, 308577, 29217, -212703, 29217, -212703, 29217, 308577, 29217, 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[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K sign,tabl,uned

%O 0,8

%A _Roger L. Bagula_, Apr 16 2010