A356206 T(n,k) are the denominators of the coefficients of the Legendre polynomials of degree n, with increasing exponents, where T(n,k) is a triangle read by rows.

1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 8, 1, 4, 1, 8, 1, 8, 1, 4, 1, 8, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 128, 1, 32, 1, 64, 1, 32, 1, 128, 1, 128, 1, 32, 1, 64, 1, 32, 1, 128, 256, 1, 256, 1, 128, 1, 128, 1, 256, 1, 256, 1, 256, 1, 256, 1, 128, 1, 128, 1, 256, 1, 256

Offset

0,4

Links

Table of n, a(n) for n=0..77.

Example

The triangle begins:
    1;
    1,   1;
    2,   1,  2;
    1,   2,  1,  2;
    8,   1,  4,  1,  8;
    1,   8,  1,  4,  1,  8;
   16,   1, 16,  1, 16,  1, 16;
    1,  16,  1, 16,  1, 16,  1, 16;
  128,   1, 32,  1, 64,  1, 32,  1, 128;
    1, 128,  1, 32,  1, 64,  1, 32,   1, 128

Prog

(PARI) for (n=0, 15, my(P=pollegendre(n, 'x)); for (j=0, n, print1(denominator(polcoef(P, j)), ", ")); print())

Crossrefs

A356205 are the corresponding numerators.

Sequence in context: A230287 A336336 A168580 * A318707 A363228 A235726

Adjacent sequences: A356203 A356204 A356205 * A356207 A356208 A356209

Keyword

nonn,frac,tabl

Author

Hugo Pfoertner, Jul 29 2022

Status

approved