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 A015740 #21 May 16 2020 21:00:53
%S A015740 0,0,0,0,1,1,1,2,2,2,3,4,4,6,8,9,11,14,16,19,23,27,32,38,45,53,62,72,
%T A015740 84,97,112,130,150,172,199,228,260,298,340,386,440,500,566,642,727,
%U A015740 820,926,1044,1174,1321,1484,1664,1866,2090
%N A015740 Number of 5's in all the partitions of n into distinct parts.
%H A015740 Vaclav Kotesovec, <a href="/A015740/b015740.txt">Table of n, a(n) for n = 1..10000</a>
%F A015740 G.f.: x^5*product(j>=1, 1+x^j )/(1+x^5). - _Emeric Deutsch_, Apr 17 2006
%F A015740 Corresponding g.f. for "number of k's" is x^k/(1+x^k)*prod(n>=1, 1+x^n ). [_Joerg Arndt_, Feb 20 2014]
%F A015740 a(n) ~ exp(Pi*sqrt(n/3)) / (8*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Oct 30 2015
%e A015740 a(9)=2 because in the 8 (=A000009(9)) partitions of 9 into distinct parts, namely [9],[8,1],[7,2],[6,3],[6,2,1],[5,4],[5,3,1] and [4,3,2] we have altogether two parts equal to 5.
%p A015740 g:=x^5*product(1+x^j,j=1..60)/(1+x^5): gser:=series(g,x=0,57): seq(coeff(gser,x,n),n=1..54); # _Emeric Deutsch_, Apr 17 2006
%t A015740 nmax = 100; Rest[CoefficientList[Series[x^5/(1+x^5) * Product[1+x^k, {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Oct 30 2015 *)
%t A015740 Table[Count[Flatten@Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], 5], {n, 54}] (* _Robert Price_, May 16 2020 *)
%K A015740 nonn
%O A015740 1,8
%A A015740 _Clark Kimberling_