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A136668
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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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1
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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, -6608, 0, 3840, 0, -1409, 0, 24032, 0, -81984, 0, 46080, 384, 0, -32798, 0, 389312, 0, -1178496, 0, 645120, 0, 18825, 0, -741056, 0, 6966848, 0, -19270656, 0, 10321920
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OFFSET
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1,4
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COMMENTS
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Row sums: {1, 1, 0, -3, -18, -129, -1182, -13281, -176478, -2704119, -46909362, ...}.
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REFERENCES
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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.
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LINKS
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FORMULA
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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.
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EXAMPLE
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Triangle begins as:
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, -6608, 0, 3840;
0, -1409, 0, 24032, 0, -81984, 0, 46080;
....
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MATHEMATICA
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P[x, 0]= 1; P[x, 1]= 1/x;
P[x_, n_]:= P[x, n] = 2*(n-1)*P[x, n-1]/x - n*P[x, n-2];
Table[ExpandAll[P[x, n] /. x -> 1/y], {n, 0, 10}];
Table[CoefficientList[P[x, n] /. x -> 1/y, y], {n, 0, 10}]//Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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