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A362899 Array read by antidiagonals: T(n,k) is the number of nonisomorphic multisets of fixed-point-free endofunctions on an n-set with k endofunctions. 4
1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 9, 6, 1, 1, 0, 1, 22, 162, 13, 1, 1, 0, 1, 63, 3935, 4527, 40, 1, 1, 0, 1, 136, 81015, 1497568, 172335, 100, 1, 1, 0, 1, 302, 1369101, 384069023, 883538845, 7861940, 291, 1, 1, 0, 1, 580, 19601383, 78954264778, 3450709120355, 725601878962, 416446379, 797, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,14
COMMENTS
Isomorphism is up to permutation of the elements of the n-set. Each endofunction can be considered to be a loopless digraph where each node has out-degree 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals).
EXAMPLE
Array begins:
==============================================================
n/k| 0 1 2 3 4 5 ...
---+----------------------------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 1 0 0 0 0 0 ...
2 | 1 1 1 1 1 1 ...
3 | 1 2 9 22 63 136 ...
4 | 1 6 162 3935 81015 1369101 ...
5 | 1 13 4527 1497568 384069023 78954264778 ...
6 | 1 40 172335 883538845 3450709120355 10786100835304758 ...
...
PROG
(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
K(v, m) = {prod(i=1, #v, my(g=gcd(v[i], m), e=v[i]/g); (sum(j=1, #v, my(t=v[j]); if(e%(t/gcd(t, m))==0, t)) - 1)^g)}
T(n, k) = {if(n==0, 1, my(s=0); forpart(q=n, s+=permcount(q) * polcoef(exp(sum(m=1, k, K(q, m)*x^m/m, O(x*x^k))), k)); s/n!)}
CROSSREFS
Columns k=0..3 are A000012, A001373, A362900, A362901.
Main diagonal is A362902.
Sequence in context: A331508 A097608 A331126 * A168261 A180997 A143439
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, May 10 2023
STATUS
approved

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Last modified February 28 19:33 EST 2024. Contains 370400 sequences. (Running on oeis4.)