A353996
Rooted simple digraphs on n unlabeled vertices.
Original entry on oeis.org
1, 4, 36, 752, 45960, 9133760, 6154473664, 14334221970688, 117222686206799936, 3412369204476033220608, 357745172369222114451432448, 136400229481294592916607770361856, 190697841181900458854914389940360337408
Offset: 1
-
with(Iterator):
RootedDig := proc(n)
local i,j,ptn,ans,a,orb2,orb4,hasptn,nextptn;
(hasptn,nextptn) := ModuleIterator(PartitionPartCount(n-1));
ans := 0;
while hasptn() do
ptn := nextptn();
a := 1 / mul(j^ptn[j]*ptn[j]!,j=1..n-1);
orb2 := add(ptn[j],j=2..n-1,2);
orb4 := add(ptn[j]*j/2,j=2..n-1,2)
+ add(ptn[j]*(j+1)/2,j=1..n-1,2)
+ add(ptn[j]*(ptn[j]-1)*j/2,j=1..n-1)
+ add(add(ptn[i]*ptn[j]*igcd(i,j),i=1..j-1),j=2..n-1);
ans := ans + a*2^orb2*4^orb4;
end do;
ans;
end proc;
A383617
Triangle read by rows: T(n,k) is the number of binary relations on a set of n objects, k of which are picked out, 0 <= k <= n.
Original entry on oeis.org
1, 2, 2, 10, 16, 10, 104, 272, 272, 104, 3044, 11456, 16960, 11456, 3044, 291968, 1432608, 2842304, 2842304, 1432608, 291968, 96928992, 578431232, 1441700480, 1920352256, 1441700480, 578431232, 96928992, 112282908928, 784780122880, 2351993457920, 3918054495616, 3918054495616, 2351993457920, 784780122880, 112282908928
Offset: 0
Triangle starts:
1;
2, 2;
10, 16, 10;
104, 272, 272, 104;
3044, 11456, 16960, 11456, 3044;
291968, 1432608, 2842304, 2842304, 1432608, 291968;
96928992, 578431232, 1441700480, 1920352256, 1441700480, ...
112282908928, 784780122880, 2351993457920, 3918054495616, 3918054495616, ...
...
Example n=2, k=1: The both objects are differentiated. As a consequence all binary relations on two different objects have to be counted: These are the subsets of the cross product of the objects set with itself. This contains four pairs, so the number of subsets is 2^4 = 16.
A384105
Triangle read by rows: T(n,k) is the number of binary relations on a set of n objects, exactly k of which are self referencing, 0 <= k <= n.
Original entry on oeis.org
1, 1, 1, 3, 4, 3, 16, 36, 36, 16, 218, 752, 1104, 752, 218, 9608, 45960, 90416, 90416, 45960, 9608, 1540944, 9133760, 22692704, 30194176, 22692704, 9133760, 1540944, 882033440, 6154473664, 18425858880, 30679088480, 30679088480, 18425858880, 6154473664, 882033440
Offset: 0
Triangle starts:
1
1, 1
3, 4, 3
16, 36, 36, 16
218, 752, 1104, 752, 218
9608, 45960, 90416, 90416, 45960, ...
1540944, 9133760, 22692704, 30194176, 22692704, ...
882033440, 6154473664, 18425858880, 30679088480, 30679088480, ...
1793359192848, 14334221970688, 50138592081152, 100240050239744, 125284653092864, ...
...
Showing 1-3 of 3 results.
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