OFFSET
1,5
COMMENTS
Row sums:
{1,0, -1, 1, 10, 4, -80, -128, 652, 2104, -5336, -32360}
REFERENCES
Defined :page 8 and pages 42 - 43 and page 49: Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986
FORMULA
The Hermite Integral form is: IH[x,n]=(x*H[x,n]-H'[x,n])/n Which can be done as an integer form: n*IH[x,n]
EXAMPLE
{1},
{-1, 1},
{0, -2, 1},
{5, -2, -3, 1},
{0, 18, -5, -4, 1},
{-33, 8, 42, -9, -5, 1},
{0, -174, 33,80, -14, -6, 1},
{279, -48, -555, 87, 135, -20, -7, 1},
{0, 1950, -279, -1380, 185, 210, -27, -8, 1},
{-2895,384, 7920, -975, -2940, 345, 308, -35, -9, 1},
{0, -25290, 2895, 24360, -2640, -5628, 588, 432, -44, -10, 1},
{35685, -3840, -125055,12645, 62790, -6090, -9954, 938, 585, -54, -11, 1}
MATHEMATICA
P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = x*P[x, n - 1] - n*P[x, n - 2]; DP[x_, n_] := D[P[x, n + 1], x]; Table[ExpandAll[x*P[x, n] - DP[x, n]], {n, 0, 10}]; a = Join[{{1}}, Table[CoefficientList[x*P[x, n] - DP[x, n], x], {n, 0, 10}]]; Flatten[a]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 18 2008
STATUS
approved