A269302 Normalization coefficients for quantum Pascal's pyramid, denominators of: T(n,k,m) = ((n - m)! m!)/(2^n (n - k)! k!).

1, 2, 2, 2, 2, 4, 8, 4, 2, 4, 2, 4, 8, 4, 8, 24, 24, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 24, 24, 8, 16, 64, 96, 64, 16, 4, 16, 24, 16, 4, 8, 32, 16, 32, 8, 4, 16, 24, 16, 4, 16, 64, 96, 64, 16, 32, 160, 320, 320, 160, 32, 32, 32, 64, 64, 32, 32, 16, 16, 32, 32, 16, 16, 16, 16, 32, 32, 16, 16, 32, 32, 64, 64, 32, 32, 32, 160, 320, 320, 160, 32

Offset

0,2

Comments

Read by block by row, i.e., a( x(n,k,m) ) have x(n,k,m) = ( sum_{i=0}^n i^2 ) + k ( n + 1 ) + m and (n,k,m) >= 0. See comments in A268533 for relevance.

Links

Table of n, a(n) for n=0..90.

Formula

T(n,k,m) = Denominator[((n - m)! m!)/(2^n (n - k)! k!)]

Example

First few blocks:
1
. . 2, 2
. . 2, 2
. . . . .  4, 8, 4
. . . . .  2, 4, 2
. . . . .  4, 8, 4

Mathematica

NormFrac[Block_] :=
Outer[Function[{n, k, m}, ((n - m)! m!)/(2^n (n - k)! k!)][
    Block, #1, #2] &, Range[0, Block], Range[0, Block], 1]; Flatten[
Denominator[NormFrac[#]] & /@ Range[0, 5]]

Crossrefs

Numerators: A269301. Cf. A268533.

Sequence in context: A364811 A244459 A064849 * A132189 A162799 A034585

Adjacent sequences: A269299 A269300 A269301 * A269303 A269304 A269305

Keyword

nonn,frac

Author

Bradley Klee, Feb 22 2016

Status

approved