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 A213268 Denominators of the Inverse semi-binomial transform of A001477(n) read downwards antidiagonals. 4
 1, 1, 1, 1, 2, 1, 1, 1, 4, 4, 1, 2, 2, 8, 2, 1, 1, 4, 1, 16, 16, 1, 2, 1, 8, 8, 32, 16, 1, 1, 4, 4, 16, 8, 64, 64, 1, 2, 2, 8, 4, 32, 32, 128, 16, 1, 1, 4, 2, 16, 16, 64, 8, 256, 256, 1, 2, 1, 8, 8, 32, 4, 128, 128, 512, 256, 1, 1, 4, 4, 16, 2, 64, 64, 256, 128, 1024, 1024 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Starting from any sequence a(k) in the first row, define the array T(n,k) of the inverse semi-binomial transform  by T(0,k) = a(k), T(n,k) = T(n-1,k+1) -T(n-1,k)/2, n>=1. Here, where the first row is the nonnegative integers, the array is 0        1      2      3    4      5      6      7     8   =A001477(n) 1       3/2     2    5/2    3    7/2      4    9/2     5   =A026741(n+2)/A000034(n) 1       5/4   3/2    7/4    2    9/4    5/2   11/4     3   =A060819(n+4)/A176895(n) 3/4     7/8     1    9/8  5/4   11/8    3/2   13/8   7/4   =A106609(n+6)/A205383(n+6) 1/2    9/16   5/8  11/16  3/4  13/16    7/8  15/16     1   =A106617(n+8)/TBD 5/16  11/32   3/8  13/32 7/16  15/32    1/2  17/32  9/16 3/16  13/64  7/32  15/64  1/4  17/64   9/32  19/64  5/16 7/64 15/128   1/8 17/128 9/64 19/128   5/32 21/128 11/64 1/16 17/256 9/128 19/256 5/64 21/256 11/128 23/256  3/32. The first column contains 0, followed by fractions A000265/A084623, that is Oresme numbers n/2^n multiplied by 2 (see A209308). LINKS EXAMPLE The array of denominators starts:   1   1   1   1   1   1   1   1   1   1   1 ...   1   2   1   2   1   2   1   2   1   2   1 ...   1   4   2   4   1   4   2   4   1   4   2 ...   4   8   1   8   4   8   2   8   4   8   1 ...   2  16   8  16   4  16   8  16   1  16   8 ... 16  32   8  32  16  32   2  32  16  32   8 ... 16  64  32  64   4  64  32  64  16  64  32 ... 64 128   8 128  64 128  32 128  64 128  16 ... 16 256 128 256  64 256 128 256  32 256 128 ... 256 512 128 512 256 512  64 512 256 512 128 ... All entries are powers of 2. MAPLE A213268frac := proc(n, k)         if n = 0 then                 return k ;         else                 return procname(n-1, k+1)-procname(n-1, k)/2 ;         end if; end proc: A213268 := proc(n, k)         denom(A213268frac(n, k)) ; end proc: # R. J. Mathar, Jun 30 2012 MATHEMATICA T[0, k_] := k; T[n_, k_] := T[n, k] = T[n-1, k+1] - T[n-1, k]/2; Table[T[n-k, k] // Denominator, {n, 0, 11}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Sep 12 2014 *) CROSSREFS Sequence in context: A290529 A266349 A219094 * A291118 A245184 A284414 Adjacent sequences:  A213265 A213266 A213267 * A213269 A213270 A213271 KEYWORD nonn,frac,tabl AUTHOR Paul Curtz, Jun 08 2012 STATUS approved

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Last modified September 24 21:05 EDT 2021. Contains 347651 sequences. (Running on oeis4.)