A036047 - OEIS

%I #7 Sep 17 2019 00:55:51

%S 1,1,1,1,1,4,12,16,392,34,48,3244032,12060,27540,6272,501696,846000,

%T 119448,4067265600,422072987719680,4338692557056,28944689875920,

%U 1247499918000000,43692593457240000,118467674601420800,422997472353189888000,56671603019312949732556800000

%N Product of order of cycles of the permutation created by duality and reversal on the partitions of n.

%o (PARI)

%o Dual(v)={my(u=vectorsmall(v[1]), k=0); forstep(i=#u, 1, -1, while(k<#v&&v[k+1]>=i,k++); u[i]=k); u}

%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=vector(#u, i, vecsearch(u, Dual(u[#u+1-i])))); vecprod(OrderCycs(v))} \\ _Andrew Howroyd_, Sep 16 2019

%Y Cf. A036045-A036056.

%K nonn

%O 1,6

%A _Olivier Gérard_

%E a(26)-a(27) from _Andrew Howroyd_, Sep 16 2019