A360653 Irregular table read by rows; the first row contains the value 1, and for n > 1, the n-th row lists the numbers of the form binomial(m-1, k) such that binomial(m, k) = n.

1, 1, 1, 2, 1, 3, 1, 4, 1, 3, 5, 1, 6, 1, 7, 1, 8, 1, 4, 6, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 5, 10, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 10, 19, 1, 6, 15, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26, 1, 7, 21, 27, 1, 28, 1, 29, 1, 30, 1, 31, 1, 32, 1, 33, 1, 15, 20, 34

Offset: 1

Author

Rémy Sigrist, Feb 15 2023

Keywords

• nonn
• tabf

Comments

In other words, the n-th rows lists the numbers that appear directly above n in Pascal's triangle (A007318).

The n-th row starts with 1, ends with n-1 (provided that n > 1), and contains other values iff n belongs to A006987.

Examples

			Table begins:
  n   n-th row
  --  -------------
   1  1
   2  1
   3  1, 2
   4  1, 3
   5  1, 4
   6  1, 3, 5
   7  1, 6
   8  1, 7
   9  1, 8
  10  1, 4, 6, 9
  11  1, 10
.
For n = 6:
    Pascal's triangle begins as follows:
                     1
                   1   1
                 1   2   1
               1   3   3   1
             1   4   6   4   1
           1   5  10  10   5   1
         1   6  15  20  15   6   1
    we find the value 6 in row 4 below 3 and 3, and in row 6 below 1 and 5,
    so the 6th row contains 1, 3 and 5.
		

Links

• Rémy Sigrist, PARI program
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A003016, A006987, A007318, A360654, A360655.

Programs

PARI

See Links section.