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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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,19 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 FORMULA T(n,k,m) = Numerator[((n - m)! m!)/(2^n (n - k)! k!)] EXAMPLE First nontrivial block: 1, 1, 1, 1 3, 1, 1, 3 3, 1, 1, 3 1, 1, 1, 1 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]] CROSSREFS Denominators: A269302. Cf. A268533. Sequence in context: A169941 A099545 A300867 * A132429 A046540 A123191 Adjacent sequences:  A269298 A269299 A269300 * A269302 A269303 A269304 KEYWORD nonn,frac AUTHOR Bradley Klee, Feb 22 2016 STATUS approved

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Last modified June 17 05:23 EDT 2021. Contains 345080 sequences. (Running on oeis4.)