login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239771 Number of pairs of functions (f,g) from a size n set into itself satisfying f(x) = g(g(f(x))). 4
1, 1, 10, 213, 8056, 465945, 37823616, 4075467781, 560230714240, 95369455852497, 19643693349548800, 4805295720474420501, 1374890520609054683136, 454286686896040037996905, 171479277693049020232695808, 73262491601904459123264721125, 35143072854722729593790081499136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

FORMULA

a(n) = Sum_{k=0..n} C(n,k) * A048993(n,k) * k! * A245348(n,k). - Alois P. Heinz, Jul 18 2014

MAPLE

g:= proc(n) g(n):= `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:

a:= n-> add(binomial(n, k)*Stirling2(n, k)*k!*

        add(binomial(n-k, i)*binomial(k, i)*i!*

        g(k-i)*n^(n-k-i), i=0..min(k, n-k)), k=0..n):

seq(a(n), n=0..20);  # Alois P. Heinz, Jul 18 2014

MATHEMATICA

g[n_] := g[n] = If[n < 2, 1, g[n-1] + (n-1)*g[n-2]];

a[n_] := If[n == 0, 1, Sum[Binomial[n, k]*StirlingS2[n, k]*k!*Sum[ Binomial[n-k, i]*Binomial[k, i]*i!*g[k-i]*n^(n-k-i), {i, 0, Min[k, n-k]} ], {k, 0, n}]];

a /@ Range[0, 20] (* Jean-Fran├žois Alcover, Oct 03 2019, after Alois P. Heinz *)

CROSSREFS

Cf. A000085, A048993, A181162, A239769, A239773, A245348, A241015.

Column k=2 of A245980.

Sequence in context: A057408 A280903 A239770 * A245987 A332408 A245981

Adjacent sequences:  A239768 A239769 A239770 * A239772 A239773 A239774

KEYWORD

nonn

AUTHOR

Chad Brewbaker, Mar 26 2014

EXTENSIONS

a(6)-a(7) from Giovanni Resta, Mar 28 2014

a(8)-a(16) from Alois P. Heinz, Jul 18 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 17 19:38 EDT 2022. Contains 356189 sequences. (Running on oeis4.)