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A305824 Number of endofunctions on [n] whose cycle lengths are triangular numbers. 6
1, 1, 3, 18, 157, 1776, 24807, 413344, 8004537, 176630400, 4374300331, 120136735104, 3623854678677, 119102912981248, 4236492477409935, 162152320065532416, 6645233337842716273, 290321208589666369536, 13469914225467040015827, 661442143465113960448000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..386

MAPLE

b:= proc(n) option remember; local r, f, g;

      if n=0 then 1 else r, f, g:=$0..2;

      while f<=n do r, f, g:= r+(f-1)!*

         b(n-f)*binomial(n-1, f-1), f+g, g+1

      od; r fi

    end:

a:= n-> add(b(j)*n^(n-j)*binomial(n-1, j-1), j=0..n):

seq(a(n), n=0..20);

MATHEMATICA

b[n_] := b[n] = Module[{r, f, g}, If[n == 0, 1, {r, f, g} = {0, 1, 2}; While[f <= n, {r, f, g} = {r + (f - 1)!*b[n - f]*Binomial[n - 1, f - 1], f + g, g + 1}]; r]];

a[0] = 1; a[n_] := Sum[b[j]*n^(n - j)*Binomial[n - 1, j - 1], {j, 0, n}];

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Jun 15 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A000217, A060435, A116956, A193374, A205799, A273994, A273996, A273998.

Sequence in context: A060913 A246523 A246529 * A116956 A166887 A075678

Adjacent sequences:  A305821 A305822 A305823 * A305825 A305826 A305827

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 10 2018

STATUS

approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)