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A362897 Array read by antidiagonals: T(n,k) is the number of nonisomorphic multisets of endofunctions on an n-set with k endofunctions. 3
1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 7, 1, 1, 1, 13, 74, 19, 1, 1, 1, 22, 638, 1474, 47, 1, 1, 1, 34, 4663, 118949, 41876, 130, 1, 1, 1, 50, 28529, 7643021, 42483668, 1540696, 343, 1, 1, 1, 70, 151600, 396979499, 33179970333, 23524514635, 68343112, 951, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
Isomorphism is up to permutations of the elements of the n-set.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals).
FORMULA
T(0,k) = T(1,k) = 1.
EXAMPLE
Array begins:
======================================================================
n/k| 0 1 2 3 4 5 ...
---+------------------------------------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 ...
2 | 1 3 7 13 22 34 ...
3 | 1 7 74 638 4663 28529 ...
4 | 1 19 1474 118949 7643021 396979499 ...
5 | 1 47 41876 42483668 33179970333 20762461502595 ...
6 | 1 130 1540696 23524514635 274252613077267 2559276179593762172 ...
...
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))^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, A001372, A054745, A362898.
Row n=2 is A002623.
Main diagonal is A277839.
Cf. A362644.
Sequence in context: A081297 A110180 A328718 * A005765 A360289 A343717
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, May 10 2023
STATUS
approved

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Last modified February 22 21:30 EST 2024. Contains 370265 sequences. (Running on oeis4.)