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.

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

Author

Roger L. Bagula, Oct 06 2006

Keywords

• tabf
• sign

Comments

Row sums give A093856.

Examples

			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;
		

References

• Eugene Jahnke and Fritz Emde, Table of Functions with Formulae and Curves, Dover Book, New York, 1945, page 144.

Links

• G. C. Greubel, Rows n = 0..30 of triangle, flattened

Crossrefs

Cf. A093856.

Programs

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

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.

Extensions

Edited by G. C. Greubel, Nov 22 2019