A360653 - OEIS

%I #10 Feb 16 2023 05:06:40

%S 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,

%T 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,

%U 26,1,7,21,27,1,28,1,29,1,30,1,31,1,32,1,33,1,15,20,34

%N 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.

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

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

%H Rémy Sigrist, <a href="/A360653/a360653.gp.txt">PARI program</a>

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%e Table begins:

%e   n   n-th row

%e   --  -------------

%e    1  1

%e    2  1

%e    3  1, 2

%e    4  1, 3

%e    5  1, 4

%e    6  1, 3, 5

%e    7  1, 6

%e    8  1, 7

%e    9  1, 8

%e   10  1, 4, 6, 9

%e   11  1, 10

%e .

%e For n = 6:

%e     Pascal's triangle begins as follows:

%e                      1

%e                    1   1

%e                  1   2   1

%e                1   3   3   1

%e              1   4   6   4   1

%e            1   5  10  10   5   1

%e          1   6  15  20  15   6   1

%e     we find the value 6 in row 4 below 3 and 3, and in row 6 below 1 and 5,

%e     so the 6th row contains 1, 3 and 5.

%o (PARI) See Links section.

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

%K nonn,tabf

%O 1,4

%A _Rémy Sigrist_, Feb 15 2023