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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-François 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.)