%I #10 Feb 16 2023 05:06:49
%S 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 6,20,105,1,120,1,136,1,153,1,171,1,15,190,1,7,35,210,1,231,1,253,1,
%U 276,1,300,1,325,1,351,1,8,56,378,1,406,1,435,1,465,1,496
%N 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 In other words, the n-th rows lists the numbers horizontally adjacent to n in Pascal's triangle (A007318).
%C The n-th contains 1 and A000217(n-1).
%H Rémy Sigrist, <a href="/A360654/a360654.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 2 1
%e 3 1, 3
%e 4 1, 6
%e 5 1, 10
%e 6 1, 4, 15
%e 7 1, 21
%e 8 1, 28
%e 9 1, 36
%e 10 1, 5, 10, 45
%e 11 1, 55
%e 12 1, 66
%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 between 4 and 4, and in row 6 between 1 and 15,
%e so the 6th row contains 1, 4 and 15.
%o (PARI) See Links section.
%Y Cf. A000217, A007318, A360653, A360655.
%K nonn,tabf
%O 2,3
%A _Rémy Sigrist_, Feb 15 2023