This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340492 #54 Feb 03 2021 23:32:47
%S A340492 1,4,12,35,84,209,450,990,2010,4074,7784,15015,27472,50355,89408,
%T A340492 158004,271755,466620,782530,1308549,2149488,3513012,5657540,9076725,
%U A340492 14367804,22645056,35313320,54810756,84269900,129032100,195879618,296147379,444466260,664284530,986341059,1458941412
%N A340492 a(n) = A000041(n)*A000070(n-1), n >= 1.
%C A340492 Conjecture: a(n) is the size of a table of correspondence between the divisors of certain numbers and the partitions of n. The table contains A006128(n) positive integers and the rest are zeros (or empty cells). These positive integers can be interpreted in two ways as follows:
%C A340492 1) They are all divisors of all terms of the first n rows of triangle A336811. In other words: they are all divisors of the first A000070(n-1) terms of A336811, hence they are all divisors of all terms in the n-th row of A176206.
%C A340492 2) They are all parts of all partitions of n.
%C A340492 The mentioned divisors are in the columns of the table.
%C A340492 The mentioned partitions are in the rows of the table.
%C A340492 For more information about the main conjecture see A336811.
%e A340492 Illustration of initial terms:
%e A340492 A000070: 1 2 4 7 12 19 30
%e A340492 A000041 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A340492 1 |_| | | | | | |
%e A340492 2 |_ _| | | | | |
%e A340492 3 |_ _ _ _| | | | |
%e A340492 | | | | |
%e A340492 5 |_ _ _ _ _ _ _| | | |
%e A340492 | | | |
%e A340492 7 |_ _ _ _ _ _ _ _ _ _ _ _| | |
%e A340492 | | |
%e A340492 | | |
%e A340492 | | |
%e A340492 11 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
%e A340492 | |
%e A340492 | |
%e A340492 | |
%e A340492 15 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e A340492 ...
%e A340492 a(n) is the area (or the number of cells) in the n-th rectangle of the diagram.
%e A340492 For n = 3 the third rectangle of the diagram contains 3*4 = 12 cells, so a(3) = 12
%e A340492 For n = 7 the seventh rectangle of the diagram contains 15*30 = 450 cells, so a(7) = 450.
%t A340492 a[n_] := PartitionsP[n]*Count[Flatten[IntegerPartitions[n]], 1]; Table[a[n], {n, 1, 36}] (* _Robert P. P. McKone_, Jan 28 2021 *)
%o A340492 (PARI) a(n) = numbpart(n)*sum(k=0, n-1, numbpart(k)); \\ _Michel Marcus_, Jan 28 2021
%Y A340492 Partial sums of A340493.
%Y A340492 Cf. A000041, A000070, A006128, A176206, A336811, A340061.
%K A340492 nonn
%O A340492 1,2
%A A340492 _Omar E. Pol_, Jan 10 2021