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 A015743 #24 Jun 15 2025 03:43:22
%S A015743 0,0,0,0,0,0,0,1,1,1,2,2,3,4,5,5,7,9,10,13,15,18,22,27,31,37,44,51,61,
%T A015743 71,82,95,111,128,148,171,195,225,258,295,337,384,437,497,565,639,724,
%U A015743 818,923,1042,1173,1319,1483,1665
%N A015743 Number of 8's in all the partitions of n into distinct parts.
%H A015743 David A. Corneth, <a href="/A015743/b015743.txt">Table of n, a(n) for n = 1..10000</a> (first 2000 terms from Robert Price)
%F A015743 G.f.: x^8*Product_{j>=1} (1+x^j)/(1+x^8). - _Emeric Deutsch_, Apr 17 2006
%F A015743 a(n) ~ exp(Pi*sqrt(n/3)) / (8*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Jun 15 2025
%e A015743 a(11)=2 because in the 12 (=A000009(11)) partitions of 11 into distinct parts, namely [11], [10,1], [9,2], [8,3], [8,2,1], [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2] and [5,3,2,1], altogether we have two parts equal to 8.
%p A015743 g:=x^8*product(1+x^j,j=1..60)/(1+x^8): gser:=series(g,x=0,57): seq(coeff(gser,x,n),n=1..54); # _Emeric Deutsch_, Apr 17 2006
%t A015743 Table[Count[Flatten@Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], 8], {n, 54}] (* _Robert Price_, Jun 13 2020 *)
%t A015743 nmax = 100; Rest[CoefficientList[Series[x^8/(1+x^8) * Product[(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jun 15 2025 *)
%K A015743 nonn
%O A015743 1,11
%A A015743 _Clark Kimberling_