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 A117524 #14 May 24 2018 04:22:11 %S A117524 0,0,1,0,1,2,3,3,7,8,13,17,25,32,48,59,83,108,145,183,247,310,406,512, %T A117524 659,824,1055,1307,1651,2047,2558,3146,3913,4788,5904,7202,8821,10707, %U A117524 13054,15770,19118,23027,27775,33312,40029,47835,57231,68182,81261 %N A117524 Total number of parts of multiplicity 3 in all partitions of n. %H A117524 Alois P. Heinz, <a href="/A117524/b117524.txt">Table of n, a(n) for n = 1..1000</a> %F A117524 G.f. for total number of parts of multiplicity m in all partitions of n is (x^m/(1-x^m)-x^(m+1)/(1-x^(m+1)))/Product(1-x^i,i=1..infinity). %F A117524 a(n) = Sum(k*A118806(n,k), k>=0). - _Emeric Deutsch_, Apr 29 2006 %F A117524 a(n) ~ exp(Pi*sqrt(2*n/3)) / (24*Pi*sqrt(2*n)). - _Vaclav Kotesovec_, May 24 2018 %e A117524 a(9) = 7 because among the 30 (=A000041(9)) partitions of 9 only [6,(1,1,1)],[4,2,(1,1,1)],[(3,3,3)],[3,3,(1,1,1)],[3,(2,2,2)],[(2,2,2),(1,1,1)] contain parts of multiplicity 3 and their total number is 7 (shown between parentheses) %p A117524 g:=(x^3/(1-x^3)-x^4/(1-x^4))/product(1-x^i,i=1..65): gser:=series(g,x=0,62): seq(coeff(gser,x,n),n=1..58); # _Emeric Deutsch_, Apr 29 2006 %Y A117524 Cf. A024786, A116646. Column k=3 of A197126. %K A117524 easy,nonn %O A117524 1,6 %A A117524 _Vladeta Jovovic_, Apr 26 2006