A268533 -id:A268533 - cp's OEIS frontend

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

Bradley Klee, Feb 22 2016

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.

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

Denominators: A269302. Cf. A268533.

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]]

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

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

Original entry on oeis.org

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

Bradley Klee, Feb 22 2016

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.

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

Numerators: A269301. Cf. A268533.

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]]

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

cp's OEIS Frontend

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

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