A269301 Normalization coefficients for quantum Pascal's pyramid, numerators of: T(n,k,m) = ((n - m)! m!)/(2^n (n - k)! k!).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Bradley Klee, Feb 22 2016

Keywords

• nonn
• frac

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.

Examples

			First nontrivial block:
1, 1, 1, 1
3, 1, 1, 3
3, 1, 1, 3
1, 1, 1, 1
		

Crossrefs

Denominators: A269302. Cf. A268533.

Programs

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[
Numerator[NormFrac[#]] & /@ Range[0, 5]]

Formula

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