OFFSET
1,5
COMMENTS
Row sums are {0, 0, 0, -15, 1, -399, -399, -14399, -78399, -639999, -12959999}.
REFERENCES
Defined: page 8 and pages 42 - 43: Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986
G. B. Shabat and I. A. Voevodskii, Drawing curves over number fields, The Grothendieck Festschift, vol. 3, Birkhäuser, 1990, pp. 199-22
LINKS
G. B. Shabat and A. Zvonkin, Plane trees and algebraic numbers, Contemporary Math., 1994, vol. 178, 233-275.
FORMULA
out=1-A137286(x,n)^2; p(x,n)=x*p(x,n-1)-p(x,n-2); q(x,n)=1-p(x,n)^2.
EXAMPLE
The irregular triangle begins
{0},
{1, 0, -1},
{-3, 0, 4, 0, -1},
{1, 0, -25, 0, 10, 0, -1},
{-63, 0, 144, 0, -97, 0, 18, 0, -1},
{1, 0, -1089, 0, 924, 0, -262,0, 28, 0, -1},
{-2303, 0, 8352, 0, -9489, 0, 3576, 0, -574, 0, 40, 0, -1},
{1, 0, -77841, 0, 103230, 0, -49291, 0, 10548,0, -1099, 0, 54, 0, -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]; Q[x_, n_] := Q[x, n] = 1 - P[x, n]^2; Table[ExpandAll[Q[x, n]], {n, 0, 10}]; a = Join[{{0}}, Table[CoefficientList[Q[x, n], x], {n, 0, 10}]]; Flatten[a]
PROG
(PARI) polx(n) = if (n == 0, 1, if (n == 1, x, x*polx(n - 1) - n*polx(n - 2)));
tabf(nn) = {for (n = 0, nn, pol = 1 - polx(n)^2; for (i = 0, 2*n, print1(polcoeff(pol, i), ", "); ); print(); ); } \\ Michel Marcus, Feb 26 2018
CROSSREFS
KEYWORD
uned,tabf,sign
AUTHOR
Roger L. Bagula, Apr 02 2008
EXTENSIONS
Keyword changed to tabf by Michel Marcus, Feb 26 2018
STATUS
approved