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A136668 Triangle read by rows: coefficients of a Bessel polynomial recursion: P(x, n) = 2*(n-1)*P(x, n - 1)/x - n*P(x, n - 2) with substitution x -> 1/y.

%I A136668 #23 Apr 19 2019 11:09:27
%S A136668 1,0,1,-2,0,2,0,-11,0,8,8,0,-74,0,48,0,119,0,-632,0,384,-48,0,1634,0,
%T A136668 -6608,0,3840,0,-1409,0,24032,0,-81984,0,46080,384,0,-32798,0,389312,
%U A136668 0,-1178496,0,645120,0,18825,0,-741056,0,6966848,0,-19270656,0,10321920
%N A136668 Triangle read by rows: coefficients of a Bessel polynomial recursion: P(x, n) = 2*(n-1)*P(x, n - 1)/x - n*P(x, n - 2) with substitution x -> 1/y.
%C A136668 Row sums: {1, 1, 0, -3, -18, -129, -1182, -13281, -176478, -2704119, -46909362, ...}.
%D A136668 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1972, 10th edition, (and various reprintings), p. 631.
%H A136668 G. C. Greubel, <a href="/A136668/b136668.txt">Table of n, a(n) for the first 25 rows, flattened</a>
%F A136668 P(x,0) = 1; P(x,1) = 1/x; P(x, n) = 2*(n-1)*P(x, n - 1)/x - n*P(x, n - 2); with substitution of x to 1/y.
%e A136668 Triangle begins as:
%e A136668     1;
%e A136668     0,     1;
%e A136668    -2,     0,    2;
%e A136668     0,   -11,    0,     8;
%e A136668     8,     0,  -74,     0,    48;
%e A136668     0,   119,    0,  -632,     0,    384;
%e A136668   -48,     0, 1634,     0, -6608,      0, 3840;
%e A136668     0, -1409,    0, 24032,     0, -81984,    0, 46080;
%e A136668     ....
%t A136668 P[x, 0]= 1; P[x, 1]= 1/x;
%t A136668 P[x_, n_]:= P[x, n] = 2*(n-1)*P[x, n-1]/x - n*P[x, n-2];
%t A136668 Table[ExpandAll[P[x, n] /. x -> 1/y], {n, 0, 10}];
%t A136668 Table[CoefficientList[P[x, n] /. x -> 1/y, y], {n, 0, 10}]//Flatten
%Y A136668 Cf. A106174, A123956.
%K A136668 tabl,sign
%O A136668 1,4
%A A136668 _Roger L. Bagula_, Apr 03 2008