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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
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
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-François Alcover, Jun 01 2018, from Maple *)
CROSSREFS
Column k=10 of A185105.
Sequence in context: A228259 A229407 A270502 * A011812 A226848 A022231
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 15 2017
STATUS
approved