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A036046 Product of the lengths of the cycle types of the permutation created by duality and reversal on the partitions of n. 1
1, 1, 1, 1, 1, 1, 2, 6, 16, 14, 34, 48, 8448, 4020, 9180, 6272, 125424, 846000, 119448, 24501600, 188089566720, 2828352384, 132167533680, 17821427400000, 459922036392000, 4085092227635200, 503568419468083200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

I.e. the permutation on the partitions of n which maps the k-th partition in Abramowitz and Stegun order to the k-th partition in Mathematica order. - Franklin T. Adams-Watters, Jun 14 2006

LINKS

Table of n, a(n) for n=0..26.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

EXAMPLE

a(7) = 6 = order of (1,2,3,5,4,6,8,9,7,10,12,11,13,14,15) = order of (4,5) (7,8,9) (11,12)

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(Set(OrderCycs(v)))} \\ Andrew Howroyd, Sep 17 2019

(PARI) \\ alternate program, see above for OrderCycs.

a(n)={my(v=vecsort([Vecsmall(Vecrev(p)) | p<-partitions(n)], , 1+4)); vecprod(Set(OrderCycs(v)))} \\ Andrew Howroyd, Sep 17 2019

CROSSREFS

Cf. A036045-A036056.

Sequence in context: A009487 A009806 A151708 * A080622 A082374 A085226

Adjacent sequences:  A036043 A036044 A036045 * A036047 A036048 A036049

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

Name changed to agree with data and a(0) = 1 prepended by Andrew Howroyd, Sep 17 2019

STATUS

approved

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Last modified April 1 02:00 EDT 2020. Contains 333153 sequences. (Running on oeis4.)