A036047 Product of order of cycles of the permutation created by duality and reversal on the partitions of n.

1, 1, 1, 1, 1, 4, 12, 16, 392, 34, 48, 3244032, 12060, 27540, 6272, 501696, 846000, 119448, 4067265600, 422072987719680, 4338692557056, 28944689875920, 1247499918000000, 43692593457240000, 118467674601420800, 422997472353189888000, 56671603019312949732556800000

Offset

1,6

Links

Table of n, a(n) for n=1..27.

Prog

(PARI)
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}
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)}
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

Crossrefs

Cf. A036045-A036056.

Sequence in context: A038242 A370191 A048661 * A356812 A045042 A367930

Adjacent sequences: A036044 A036045 A036046 * A036048 A036049 A036050

Keyword

nonn

Author

Olivier Gérard

Extensions

a(26)-a(27) from Andrew Howroyd, Sep 16 2019

Status

approved