login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Row sums: {1, 1, 0, -3, -18, -129, -1182, -13281, -176478, -2704119, -46909362, ...}.
REFERENCES
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.
LINKS
FORMULA
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.
EXAMPLE
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;
....
MATHEMATICA
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
CROSSREFS
Sequence in context: A300073 A113400 A089780 * A057498 A137949 A019214
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Apr 03 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)