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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.

%I A360655 #6 Feb 16 2023 05:07:02
%S A360655 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,
%T A360655 91,15,105,16,21,35,120,17,136,18,153,19,171,20,190,21,35,210,22,28,
%U A360655 56,231,23,253,24,276,25,300,26,325,27,351,28,378,29,36,84,406,30,435
%N 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.
%C A360655 In other words, the n-th rows lists the numbers that appear directly below n in Pascal's triangle (A007318).
%C A360655 The n-th row starts with n+1.
%H A360655 Rémy Sigrist, <a href="/A360655/a360655.gp.txt">PARI program</a>
%H A360655 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%e A360655 Table begins:
%e A360655   n   n-th row
%e A360655   --  --------------
%e A360655    2  3
%e A360655    3  4, 6
%e A360655    4  5, 10
%e A360655    5  6, 15
%e A360655    6  7, 10, 21
%e A360655    7  8, 28
%e A360655    8  9, 36
%e A360655    9  10, 45
%e A360655   10  11, 15, 20, 55
%e A360655   11  12, 66
%e A360655   12  13, 78
%e A360655 .
%e A360655 For n = 6:
%e A360655     Pascal's triangle begins:
%e A360655                       1
%e A360655                     1   1
%e A360655                   1   2   1
%e A360655                 1   3   3   1
%e A360655               1   4   6   4   1
%e A360655             1   5  10  10   5   1
%e A360655           1   6  15  20  15   6   1
%e A360655         1   7  21  35  35  21   7   1
%e A360655     the value 6 appears in row 3 above 10, and in row 6 above 7 and 21,
%e A360655     so the 6th row contains 7, 10 and 21.
%o A360655 (PARI) See Links section.
%Y A360655 Cf. A007318, A360653, A360654.
%K A360655 nonn,tabf
%O A360655 2,1
%A A360655 _Rémy Sigrist_, Feb 15 2023