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, 2, 6, 16, 14, 34, 48, 8448, 4020, 9180, 6272, 125424, 846000, 119448, 24501600, 188089566720, 2828352384, 132167533680, 17821427400000, 459922036392000, 4085092227635200, 503568419468083200

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: A151708 A356370 A355096 * 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