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%I #8 Sep 17 2019 14:55:46
%S 1,1,1,3,3,7,11,20,25,37,54,74,98,131,169,227,293,380,486,622,787,970,
%T 1251,1569,1946,2431,3003,3713,4544,5599,6831,8324,10139,12305,14873,
%U 17974,21632,26006,31180,37334,44575,53171,63257,75172,89132,105523,124749,147268,173520,204222
%N Sum of the lengths of the cycle types of the permutation created by length sorting on the partitions of n.
%o (PARI)
%o OrderCycs(v)={my(t=vector(#v), L=List()); for(i=1, #v, my(c=0,j=i); while(!t[j], t[j]=1; j=v[j]; c++); if(c, listput(L,c))); Vec(L)}
%o a(n)={my(u=vecsort([Vecsmall(Vecrev(p)) | p<-partitions(n)])); my(v=vecsort(u, (x,y)->lex(#x,#y), 1+4)); vecsum(Set(OrderCycs(v)))} \\ _Andrew Howroyd_, Sep 17 2019
%Y Cf. A036045-A036056.
%K nonn
%O 1,4
%A _Olivier Gérard_
%E a(31)-a(50) from _Andrew Howroyd_, Sep 17 2019
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