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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. 2

%I #15 Oct 02 2018 11:32:08

%S 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 -40,-202,-128,8,32,8,-15,-75,-60,300,765,585,-142,-470,-220,20,40,8,

%U 0,-210,-1260,-2730,-1680,2982,6132,3586,-744,-1860,-688,72,96,16,105,735,1365

%N 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 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 Triangle begins:

%e 1;

%e 0, 2;

%e -1, -1, 2, 2;

%e 0, -6, -12, -2, 8, 4;

%e 3, 9, -3, -33, -32, 0, 12, 4;

%e 0, 30, 120, 140, -40, -202, -128, 8, 32, 8;

%e -15, -75, -60, 300, 765, 585, -142, -470, -220, 20, 40, 8;

%e ... reformatted. - _Franck Maminirina Ramaharo_, Oct 02 2018

%t Join[{1},Table[CoefficientList[HermiteH[n,x]*(x + 1)^(n - 1)/2^Floor[n/2], x], {n, 1, 12}]]//Flatten

%Y Cf. A007318, A060821, A171229, A171631.

%K sign,tabf

%O 0,3

%A _Roger L. Bagula_, Dec 11 2009

%E Edited and new name by _Franck Maminirina Ramaharo_, Oct 02 2018

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Last modified September 13 11:59 EDT 2024. Contains 375907 sequences. (Running on oeis4.)