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A215562 Number of permutations of n indistinguishable copies of 1..4 with every partial sum <= the same partial sum averaged over all permutations. 2
1, 7, 403, 40350, 5223915, 783353872, 129141898872, 22745605840236, 4206489449301315, 807660192541534200, 159752979289765273698, 32371149339259024610992, 6692030708288364864188400, 1406943391115083641966787200, 300084647544974128326709244080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..133 (terms 0..60 from Alois P. Heinz)

FORMULA

a(n) ~ (phi - sqrt(phi)) * 2^(8*n-1/2) / (Pi^(3/2) * n^(5/2)), where phi = (1+sqrt(5))/2. - Vaclav Kotesovec, Jan 31 2015

EXAMPLE

a(0) = 1: the empty permutation.

a(1) = 7: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,4,2,3), (2,1,3,4), (2,1,4,3), (2,3,1,4).

a(2) = 403: (1,1,2,2,3,3,4,4), (1,1,2,2,3,4,3,4), ..., (2,3,2,3,1,1,4,4), (2,3,2,3,1,4,1,4).

MAPLE

b:= proc(l) option remember; local m, n, g;

      m, n:= nops(l), add(i, i=l);

      g:= add(i*l[i], i=1..m)-(m+1)/2*(n-1);

     `if`(n<2, 1, add(`if`(l[i]>0 and i<=g,

        b(subsop(i=l[i]-1, l)), 0), i=1..m))

    end:

a:= n-> b([n$4]):

seq(a(n), n=0..15);

CROSSREFS

Row n=4 of A215561.

Sequence in context: A015022 A225167 A160292 * A099125 A172894 A286393

Adjacent sequences:  A215559 A215560 A215561 * A215563 A215564 A215565

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 16 2012

STATUS

approved

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Last modified February 27 07:04 EST 2020. Contains 332299 sequences. (Running on oeis4.)