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A136209 Differentiation of A137286: Triangle of coefficients of differentiation recursive orthogonal Hermite polynomials given in Hochstadt's book : P(x, n) = x*P(x, n - 1) - n*P(x, n - 2).

%I A136209 #3 Mar 30 2012 17:34:22
%S A136209 1,0,2,-5,0,3,0,-18,0,4,33,0,-42,0,5,0,174,0,-80,0,6,-279,0,555,0,
%T A136209 -135,0,7,0,-1950,0,1380,0,-210,0,8,2895,0,-7920,0,2940,0,-308,0,9,0,
%U A136209 25290,0,-24360,0,5628,0,-432,0,10,-35685,0,125055,0,-62790,0,9954,0,-585,0,11
%N A136209 Differentiation of A137286: Triangle of coefficients of differentiation recursive orthogonal Hermite polynomials given in Hochstadt's book : P(x, n) = x*P(x, n - 1) - n*P(x, n - 2).
%C A136209 Row sums are:
%C A136209 {1, 2, -2, -14, -4, 100, 148, -772, -2384, 6136, 35960}
%D A136209 page 8 and pages 42 - 43 : Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986
%F A136209 P(x, n) = x*P(x, n - 1) - n*P(x, n - 2); L(x,n)=dP(x,n+1]/dx
%e A136209 {1},
%e A136209 {0, 2},
%e A136209 {-5, 0, 3},
%e A136209 {0, -18, 0, 4},
%e A136209 {33, 0, -42, 0,5},
%e A136209 {0, 174, 0, -80, 0, 6},
%e A136209 {-279, 0, 555, 0, -135, 0, 7},
%e A136209 {0, -1950, 0, 1380, 0, -210, 0, 8},
%e A136209 {2895, 0, -7920, 0, 2940, 0, -308, 0, 9},
%e A136209 {0, 25290,0, -24360, 0, 5628, 0, -432, 0, 10},
%e A136209 {-35685, 0, 125055, 0, -62790, 0,9954, 0, -585, 0, 11}
%t A136209 H[x, 0] = 1; H[x, 1] = x; H[x_, n_] := H[x, n] = x*H[x, n - 1] - n*H[x, n - 2]; L[x_, n_] := D[H[x, n + 1], x]; a0 = Table[ExpandAll[L[x, n]], {n, 0, 10}]; a = Table[CoefficientList[L[x, n], x], {n, 0, 10}]; Flatten[a]
%Y A136209 Cf. A137286.
%K A136209 uned,tabl,sign
%O A136209 1,3
%A A136209 _Roger L. Bagula_, Mar 16 2008