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A285238 Number of entries in the tenth cycles of all permutations of [n]. 2
1, 57, 2061, 61524, 1672323, 43426821, 1106667572, 28127644296, 720378419177, 18715673685469, 495446888127507, 13403690294272704, 371315688867567088, 10546557230068193568, 307378160401299252032, 9196581430595518185328, 282526394585486139996736 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,2

COMMENTS

Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..450

Wikipedia, Permutation

FORMULA

a(n) = A185105(n,10).

Recurrence: (n-10)*(n-7)*a(n) = (9*n^3 - 196*n^2 + 1361*n - 3006)*a(n-1) - 2*(18*n^4 - 496*n^3 + 5001*n^2 - 21971*n + 35682)*a(n-2) + 14*(6*n^5 - 206*n^4 + 2797*n^3 - 18829*n^2 + 63002*n - 83988)*a(n-3) - 7*(18*n^6 - 758*n^5 + 13240*n^4 - 122950*n^3 + 640883*n^2 - 1779393*n + 2057142)*a(n-4) + 7*(18*n^7 - 916*n^6 + 19950*n^5 - 241180*n^4 + 1748577*n^3 - 7604998*n^2 + 18375843*n - 19031658)*a(n-5) - (84*n^8 - 5096*n^7 + 135226*n^6 - 2050286*n^5 + 19428976*n^4 - 117838826*n^3 + 446719463*n^2 - 967742093*n + 917171710)*a(n-6) + (n-8)*(36*n^8 - 2284*n^7 + 63390*n^6 - 1005202*n^5 + 9960732*n^4 - 63153820*n^3 + 250166217*n^2 - 565970839*n + 559792740)*a(n-7) - (9*n^10 - 749*n^9 + 28038*n^8 - 621666*n^7 + 9040584*n^6 - 90096090*n^5 + 623077092*n^4 - 2952338109*n^3 + 9171809128*n^2 - 16867010733*n + 13941384550)*a(n-8) + (n-9)^10*(n-6)*a(n-9), for n>10. - Vaclav Kotesovec, Apr 25 2017

a(n) ~ n!*n/1024. - Vaclav Kotesovec, Apr 25 2017

MAPLE

b:= proc(n, i) option remember; expand(`if`(n=0, 1,

      add((p-> p+`if`(i=1, coeff(p, x, 0)*j*x, 0))(

      b(n-j, max(0, i-1)))*binomial(n-1, j-1)*

      (j-1)!, j=1..n)))

    end:

a:= n-> coeff(b(n, 10), x, 1):

seq(a(n), n=10..30);

MATHEMATICA

b[n_, i_] := b[n, i] = Expand[If[n == 0, 1, Sum[Function[p, p + If[i == 1, Coefficient[p, x, 0]*j*x, 0]][b[n - j, Max[0, i - 1]]]*Binomial[n - 1, j - 1]*(j - 1)!, {j, 1, n}]]];

a[n_] := Coefficient[b[n, 10], x, 1];

Table[a[n], {n, 10, 30}] (* Jean-Fran├žois Alcover, Jun 01 2018, from Maple *)

CROSSREFS

Column k=10 of A185105.

Sequence in context: A228259 A229407 A270502 * A011812 A226848 A022231

Adjacent sequences:  A285235 A285236 A285237 * A285239 A285240 A285241

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 15 2017

STATUS

approved

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Last modified December 4 04:22 EST 2020. Contains 338921 sequences. (Running on oeis4.)