OFFSET
7,2
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 = 7..450
Wikipedia, Permutation
FORMULA
a(n) = A185105(n,7).
Recurrence: (n-7)*(n-4)*a(n) = (n-3)*(6*n^2 - 67*n + 176)*a(n-1) - 5*(n-4)*(3*n^3 - 43*n^2 + 195*n - 283)*a(n-2) + 10*(2*n^5 - 47*n^4 + 436*n^3 - 1999*n^2 + 4532*n - 4062)*a(n-3) - (15*n^6 - 445*n^5 + 5465*n^4 - 35555*n^3 + 129161*n^2 - 248111*n + 196528)*a(n-4) + (6*n^7 - 221*n^6 + 3473*n^5 - 30165*n^4 + 156251*n^3 - 482105*n^2 + 819087*n - 589808)*a(n-5) - (n-6)^7*(n-3)*a(n-6), for n>7. - Vaclav Kotesovec, Apr 25 2017
a(n) ~ n!*n/128. - 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, 7), x, 1):
seq(a(n), n=7..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, 7], x, 1];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Jun 01 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 15 2017
STATUS
approved