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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.
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%I #23 Apr 19 2019 11:09:27

%S 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 -6608,0,3840,0,-1409,0,24032,0,-81984,0,46080,384,0,-32798,0,389312,

%U 0,-1178496,0,645120,0,18825,0,-741056,0,6966848,0,-19270656,0,10321920

%N 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 Row sums: {1, 1, 0, -3, -18, -129, -1182, -13281, -176478, -2704119, -46909362, ...}.

%D 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 G. C. Greubel, <a href="/A136668/b136668.txt">Table of n, a(n) for the first 25 rows, flattened</a>

%F 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 Triangle begins as:

%e 1;

%e 0, 1;

%e -2, 0, 2;

%e 0, -11, 0, 8;

%e 8, 0, -74, 0, 48;

%e 0, 119, 0, -632, 0, 384;

%e -48, 0, 1634, 0, -6608, 0, 3840;

%e 0, -1409, 0, 24032, 0, -81984, 0, 46080;

%e ....

%t P[x, 0]= 1; P[x, 1]= 1/x;

%t P[x_, n_]:= P[x, n] = 2*(n-1)*P[x, n-1]/x - n*P[x, n-2];

%t Table[ExpandAll[P[x, n] /. x -> 1/y], {n, 0, 10}];

%t Table[CoefficientList[P[x, n] /. x -> 1/y, y], {n, 0, 10}]//Flatten

%Y Cf. A106174, A123956.

%K tabl,sign

%O 1,4

%A _Roger L. Bagula_, Apr 03 2008