login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269302 Normalization coefficients for quantum Pascal's pyramid, denominators of: T(n,k,m) = ((n - m)! m!)/(2^n (n - k)! k!). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A060824 A244459 A064849 * A132189 A162799 A034585

Adjacent sequences:  A269299 A269300 A269301 * A269303 A269304 A269305

KEYWORD

nonn,frac

AUTHOR

Bradley Klee, Feb 22 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)