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A211880
Number of permutations of n elements with no fixed points and largest cycle of length 3.
2
0, 0, 0, 2, 0, 20, 40, 210, 1120, 4760, 25200, 157850, 800800, 5345340, 35035000, 222472250, 1648046400, 12000388400, 88529240800, 720929459250, 5786188408000, 48072795270500, 424300329453000, 3731123025279650, 34083741984292000, 323768324084205000
OFFSET
0,4
COMMENTS
a(n) = A055814(n) - A123023(n+2). - Vaclav Kotesovec, Oct 09 2013
LINKS
FORMULA
E.g.f.: (exp(x^3/3)-1) * exp(x^2/2).
Recurrence: (n-3)*a(n) = (n-1)*(2*n-5)*a(n-2) + (n-3)*(n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)*a(n-4) - (n-4)*(n-3)*(n-2)*(n-1)*a(n-5). - Vaclav Kotesovec, Oct 09 2013
EXAMPLE
a(3) = 2: (2,3,1), (3,1,2).
MAPLE
egf:= (exp(x^3/3)-1)*exp(x^2/2):
a:= n-> n! *coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..30);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n < 0, 0, If[n == 0, 1,
Sum[Product[n - i, {i, 1, j - 1}] A[n - j, k], {j, 2, k}]]];
T[n_, k_] := A[n, k] - If[k == 0, 0, A[n, k - 1]];
a[n_] := T[n, 3];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Sep 03 2021, after Alois P. Heinz in A211871 *)
CROSSREFS
Column k=3 of A211871.
Sequence in context: A139003 A264881 A280622 * A365862 A209868 A182661
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 13 2013
STATUS
approved