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A171531 Irregular triangle read by rows: first row is 1, n-th row (n > 0) consists of the coefficients in the expansion of H(x;n)*(x + 1)^(n - 1)/2^floor(n/2), where H(x;n) is the Hermite polynomial of order n.

%I A171531 #15 Oct 02 2018 11:32:08
%S A171531 1,0,2,-1,-1,2,2,0,-6,-12,-2,8,4,3,9,-3,-33,-32,0,12,4,0,30,120,140,
%T A171531 -40,-202,-128,8,32,8,-15,-75,-60,300,765,585,-142,-470,-220,20,40,8,
%U A171531 0,-210,-1260,-2730,-1680,2982,6132,3586,-744,-1860,-688,72,96,16,105,735,1365
%N A171531 Irregular triangle read by rows: first row is 1, n-th row (n > 0) consists of the coefficients in the expansion of H(x;n)*(x + 1)^(n - 1)/2^floor(n/2), where H(x;n) is the Hermite polynomial of order n.
%H A171531 Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, page 695.
%e A171531 Triangle begins:
%e A171531     1;
%e A171531     0,   2;
%e A171531    -1,  -1,   2,   2;
%e A171531     0,  -6, -12,  -2,   8,    4;
%e A171531     3,   9,  -3, -33, -32,    0,   12,    4;
%e A171531     0,  30, 120, 140, -40, -202, -128,    8,   32,  8;
%e A171531   -15, -75, -60, 300, 765,  585, -142, -470, -220, 20, 40, 8;
%e A171531    ... reformatted. - _Franck Maminirina Ramaharo_, Oct 02 2018
%t A171531 Join[{1},Table[CoefficientList[HermiteH[n,x]*(x + 1)^(n - 1)/2^Floor[n/2], x], {n, 1, 12}]]//Flatten
%Y A171531 Cf. A007318, A060821, A171229, A171631.
%K A171531 sign,tabf
%O A171531 0,3
%A A171531 _Roger L. Bagula_, Dec 11 2009
%E A171531 Edited and new name by _Franck Maminirina Ramaharo_, Oct 02 2018