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A123235
Triangle of coefficients p(k, x), where p(k, x) = 2*(k-1)*p(k-1, x) -x*p(k-2, x), read by rows.
2
1, 1, 1, 2, 1, 8, 3, -1, 48, 16, -7, 384, 120, -59, 1, 3840, 1152, -606, 17, 46080, 13440, -7392, 263, -1, 645120, 184320, -104640, 4288, -31, 10321920, 2903040, -1687680, 76000, -759, 1, 185794560, 51609600, -30562560, 1472640, -17950, 49
OFFSET
0,4
COMMENTS
Row sums give A093856.
REFERENCES
Eugene Jahnke and Fritz Emde, Table of Functions with Formulae and Curves, Dover Book, New York, 1945, page 144.
FORMULA
Coefficient list of the polynomials p(k, x) = 2*(k-1)*p(k-1, x) - x*p(k - 2, x), with p(0, x) = 1 and p(1, x) = 1 + x.
EXAMPLE
Triangle begins as:
1;
1, 1;
2, 1;
8, 3, -1;
48, 16, -7;
384, 120, -59, 1;
3840, 1152, -606, 17;
46080, 13440, -7392, 263, -1;
MATHEMATICA
p[n_, x_]:= p[n, x]= If[n==0, 1, If[n==1, x+1, 2*(n-1)*p[n-1, x] -x*p[n-2, x]]]; Table[CoefficientList[p[n, x], x], {n, 0, 10}]//Flatten
CROSSREFS
Cf. A093856.
Sequence in context: A232535 A065826 A286899 * A176052 A351560 A140273
KEYWORD
tabf,sign
AUTHOR
Roger L. Bagula, Oct 06 2006
EXTENSIONS
Edited by G. C. Greubel, Nov 22 2019
STATUS
approved