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A229789 Triangle T(n,k): the coefficient [x^(n-k)] of the polynomial 2^n*n!*L(n,3/2,x), where L is the generalized Laguerre Polynomial in the Abramowitz-Stegun normalization.

%I A229789 #13 May 15 2018 08:35:42
%S A229789 1,-2,5,4,-28,35,-8,108,-378,315,16,-352,2376,-5544,3465,-32,1040,
%T A229789 -11440,51480,-90090,45045,64,-2880,46800,-343200,1158300,-1621620,
%U A229789 675675,-128,7616,-171360,1856400,-10210200,27567540,-32162130,11486475,256,-19456,578816,-8682240,70543200,-310390080,698377680,-698377680,218243025
%N A229789 Triangle T(n,k): the coefficient [x^(n-k)] of the polynomial 2^n*n!*L(n,3/2,x), where L is the generalized Laguerre Polynomial in the Abramowitz-Stegun normalization.
%H A229789 G. C. Greubel, <a href="/A229789/b229789.txt">Rows n=0..100 of triangle, flattened</a>
%H A229789 R. J. Mathar, <a href="http://vixra.org/abs/1303.0013">Gauss-Laguerre and Gauss-Hermite quadrature on 64, 96 and 128 nodes</a>, see Hermite case with m=2.
%e A229789 2^0*0!*L(0,3/2,x) = 1;
%e A229789 2^1*1!*L(1,3/2,x) = -2*x+5;
%e A229789 2^2*2!*L(2,3/2,x) = 4*x^2 -28*x +35 ;
%e A229789 2^3*3!*L(3,3/2,x) = -8*x^3+108*x^2 -378*x +315 ;
%e A229789 2^4*4!*L(4,3/2,x) = 16*x^4 -352*x^3 +2376*x^2 -5544*x +3465 ;
%p A229789 A229789 := proc(n,k)
%p A229789     local p;
%p A229789     p := 2^n*n!*expand(L(n,3/2,x)) ;
%p A229789     coeftayl(p,x=0,n-k) ;
%p A229789 end proc:
%p A229789 seq(seq(A229789(n,k),k=0..n),n=0..10) ;
%t A229789 t[n_, k_] := Coefficient[2^n*n!*LaguerreL[n, 3/2, x], x, n-k]; Table[t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jan 09 2014 *)
%Y A229789 Cf. A098503.
%K A229789 sign,tabl
%O A229789 0,2
%A A229789 _R. J. Mathar_, Sep 29 2013