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%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
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