OFFSET
0,5
COMMENTS
LINKS
EXAMPLE
Start of triangle pf with corresponding triangles of numerators and denominators:
. 0: 1
. 1: 1 1/2
. 2: 1 3/2 1/3
. 3: 1 5/2 11/6 1/4
. 4: 1 7/2 13/3 25/12 1/5
. 5: 1 9/2 47/6 77/12 137/60 1/6
. 6: 1 11/2 37/3 57/4 87/10 49/20 1/7
. 7: 1 13/2 107/6 319/12 459/20 223/20 363/140 1/8
. 8: 1 15/2 73/3 533/12 743/15 341/10 481/35 761/280 1/9,
.
. 0: numerators 1 1 denominators
. 1: 1 1 1 2 A213999
. 2: 1 3 1 1 2 3
. 3: 1 5 11 1 1 2 6 4
. 4: 1 7 13 25 1 1 2 3 12 5
. 5: 1 9 47 77 137 1 1 2 6 12 60 6
. 6: 1 11 37 57 87 49 1 1 2 3 4 10 20 7
. 7: 1 13 107 319 459 223 363 1 1 2 6 12 20 20 140 8
. 8: 1 15 73 533 743 341 481 761 1, 1 2 3 12 15 10 35 280 9.
MATHEMATICA
T[_, 0] = 1; T[n_, n_] := 1/(n + 1);
T[n_, k_] := T[n, k] = T[n - 1, k] + T[n - 1, k - 1];
Table[T[n, k] // Numerator, {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 10 2021 *)
PROG
(Haskell)
import Data.Ratio ((%), numerator, denominator, Ratio)
a213998 n k = a213998_tabl !! n !! k
a213998_row n = a213998_tabl !! n
a213998_tabl = map (map numerator) $ iterate pf [1] where
pf row = zipWith (+) ([0] ++ row) (row ++ [-1 % (x * (x + 1))])
where x = denominator $ last row
CROSSREFS
AUTHOR
Reinhard Zumkeller, Jul 03 2012
STATUS
approved