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A360654 Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m, k-1) such that binomial(m, k) = n.

%I A360654 #10 Feb 16 2023 05:06:49
%S A360654 1,1,3,1,6,1,10,1,4,15,1,21,1,28,1,36,1,5,10,45,1,55,1,66,1,78,1,91,1,
%T A360654 6,20,105,1,120,1,136,1,153,1,171,1,15,190,1,7,35,210,1,231,1,253,1,
%U A360654 276,1,300,1,325,1,351,1,8,56,378,1,406,1,435,1,465,1,496
%N A360654 Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m, k-1) such that binomial(m, k) = n.
%C A360654 In other words, the n-th rows lists the numbers horizontally adjacent to n in Pascal's triangle (A007318).
%C A360654 The n-th contains 1 and A000217(n-1).
%H A360654 Rémy Sigrist, <a href="/A360654/a360654.gp.txt">PARI program</a>
%H A360654 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%e A360654 Table begins:
%e A360654   n   n-th row
%e A360654   --  ------------
%e A360654    2  1
%e A360654    3  1, 3
%e A360654    4  1, 6
%e A360654    5  1, 10
%e A360654    6  1, 4, 15
%e A360654    7  1, 21
%e A360654    8  1, 28
%e A360654    9  1, 36
%e A360654   10  1, 5, 10, 45
%e A360654   11  1, 55
%e A360654   12  1, 66
%e A360654 .
%e A360654 For n = 6:
%e A360654     Pascal's triangle begins as follows:
%e A360654                      1
%e A360654                    1   1
%e A360654                  1   2   1
%e A360654                1   3   3   1
%e A360654              1   4   6   4   1
%e A360654            1   5  10  10   5   1
%e A360654          1   6  15  20  15   6   1
%e A360654     we find the value 6 in row 4 between 4 and 4, and in row 6 between 1 and 15,
%e A360654     so the 6th row contains 1, 4 and 15.
%o A360654 (PARI) See Links section.
%Y A360654 Cf. A000217, A007318, A360653, A360655.
%K A360654 nonn,tabf
%O A360654 2,3
%A A360654 _Rémy Sigrist_, Feb 15 2023