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 A213998 Numerators of the triangle of fractions read by rows: pf(n,0) = 1, pf(n,n) = 1/(n+1) and pf(n+1,k) = pf(n,k) + pf(n,k-1) with 0 < k < n; denominators: A213999. 6
 1, 1, 1, 1, 3, 1, 1, 5, 11, 1, 1, 7, 13, 25, 1, 1, 9, 47, 77, 137, 1, 1, 11, 37, 57, 87, 49, 1, 1, 13, 107, 319, 459, 223, 363, 1, 1, 15, 73, 533, 743, 341, 481, 761, 1, 1, 17, 191, 275, 1879, 2509, 3349, 4609, 7129, 1, 1, 19, 121, 1207, 1627, 2131, 2761, 3601, 4861, 7381, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,0) = 1; T(n,1) = A005408(n-1) for n > 0; T(n,2) = A188386(n-2) for n > 2; T(n,n-3) = A124837(n-2) for n > 2; T(n,n-2) = A027612(n-1) for n > 1; T(n,n-1) = A001008(n) for n > 0; T(n,n) = 1; A214075(n,k) = floor(T(n,k) / A213999(n,k)). LINKS Reinhard Zumkeller, Rows n = 0..150 of triangle, flattened 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. 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 Sequence in context: A086385 A295222 A123162 * A294946 A083075 A335333 Adjacent sequences:  A213995 A213996 A213997 * A213999 A214000 A214001 KEYWORD nonn,frac,tabl,look AUTHOR Reinhard Zumkeller, Jul 03 2012 STATUS approved

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)