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

%I

%S 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,

%T 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,

%U 1,1,1,1,5,5,1,1,1,1,5,5,1,1,1,1,5,1,1,1,1,1,1

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

%C 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.

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

%e First nontrivial block:

%e 1, 1, 1, 1

%e 3, 1, 1, 3

%e 3, 1, 1, 3

%e 1, 1, 1, 1

%t NormFrac[Block_] :=

%t Outer[Function[{n, k, m}, ((n - m)! m!)/(2^n (n - k)! k!)][

%t Block, #1, #2] &, Range[0, Block], Range[0, Block], 1]; Flatten[

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

%Y Denominators: A269302. Cf. A268533.

%K nonn,frac

%O 0,19

%A _Bradley Klee_, Feb 22 2016

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)