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 A246192 Number of endofunctions on [n] where the smallest cycle length equals 5. 2
 24, 720, 17640, 430080, 11022480, 302472576, 8937981360, 284552040960, 9743091569640, 357820740076800, 14051646110285784, 588177615908413440, 26161789829441054880, 1232890909824506204160, 61387038018996808785120, 3221070809733138102829056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 5..200 FORMULA a(n) ~ (exp(-25/12) - exp(-137/60)) * n^n. - Vaclav Kotesovec, Aug 21 2014 MAPLE with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,       add((i-1)!^j*multinomial(n, n-i*j, i\$j)/j!*       b(n-i*j, i+1), j=0..n/i)))     end: A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n): a:= n-> A(n, 5) -A(n, 6): seq(a(n), n=5..25); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n==0, 1, If[i>n, 0, Sum[(i - 1)!^j multinomial[n, Join[{n - i*j}, Table[i, {j}]]]/j! b[n - i*j, i + 1], {j, 0, n/i}]]]; A[n_, k_] := Sum[Binomial[n - 1, j - 1] n^(n - j) b[j, k], {j, 0, n}]; a[n_] := A[n, 5] - A[n, 6]; a /@ Range[5, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *) CROSSREFS Column k=5 of A246049. Sequence in context: A184274 A093456 A189412 * A246612 A289635 A105187 Adjacent sequences:  A246189 A246190 A246191 * A246193 A246194 A246195 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 18 2014 STATUS approved

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Last modified December 6 17:58 EST 2021. Contains 349567 sequences. (Running on oeis4.)