A360655 Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m+1, k) such that binomial(m, k) = n.

3, 4, 6, 5, 10, 6, 15, 7, 10, 21, 8, 28, 9, 36, 10, 45, 11, 15, 20, 55, 12, 66, 13, 78, 14, 91, 15, 105, 16, 21, 35, 120, 17, 136, 18, 153, 19, 171, 20, 190, 21, 35, 210, 22, 28, 56, 231, 23, 253, 24, 276, 25, 300, 26, 325, 27, 351, 28, 378, 29, 36, 84, 406, 30, 435

Offset: 2

Author

Rémy Sigrist, Feb 15 2023

Keywords

• nonn
• tabf

Comments

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

The n-th row starts with n+1.

Examples

			Table begins:
  n   n-th row
  --  --------------
   2  3
   3  4, 6
   4  5, 10
   5  6, 15
   6  7, 10, 21
   7  8, 28
   8  9, 36
   9  10, 45
  10  11, 15, 20, 55
  11  12, 66
  12  13, 78
.
For n = 6:
    Pascal's triangle begins:
                      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
        1   7  21  35  35  21   7   1
    the value 6 appears in row 3 above 10, and in row 6 above 7 and 21,
    so the 6th row contains 7, 10 and 21.
		

Links

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

Crossrefs

Cf. A007318, A360653, A360654.

Programs

PARI

See Links section.