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A036047 Product of order of cycles of the permutation created by duality and reversal on the partitions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A066632 A038242 A048661 * A045042 A095099 A134860

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

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Last modified May 28 12:02 EDT 2020. Contains 334681 sequences. (Running on oeis4.)