A334282
Number of properly colored labeled graphs on n nodes so that the color function is surjective onto {c_1,c_2,...,c_k} for some k, 1<=k<=n.
Original entry on oeis.org
1, 1, 5, 73, 2849, 277921, 65067905, 35545840513, 44384640206849, 124697899490480641, 778525887500557625345, 10693248499002776513697793, 320453350845793018626300755969, 20807125028666778079876193487790081, 2909872870574162514727072641529432735745
Offset: 0
-
b:= proc(n, k) option remember; `if`([n, k]=[0$2], 1,
add(binomial(n, r)*2^(r*(n-r))*b(r, k-1), r=0..n-1))
end:
a:= n-> add(b(n,k), k=0..n):
seq(a(n), n=0..15); # Alois P. Heinz, Apr 21 2020
-
nn = 15; e2[x_] := Sum[x^n/(n! 2^Binomial[n, 2]), {n, 0, nn}];
Table[n! 2^Binomial[n, 2], {n, 0, nn}] CoefficientList[Series[1/(1 - (e2[x] - 1)), {x, 0, nn}], x]
A365593
Number of n X n Boolean relation matrices such that every block of its Frobenius normal form is either a 0 block or a 1 block.
Original entry on oeis.org
1, 2, 13, 219, 9322, 982243, 249233239, 148346645212, 202688186994599, 624913864623500599, 4289324010827093793808, 64841661094150427710360745, 2140002760057211517052090865983, 153082134018816602622335941790247946, 23590554099141037133024176892280338280237
Offset: 0
-
nn = 12; d[x_] :=Total[Cases[Import["https://oeis.org/A003024/b003024.txt",
"Table"], {, }][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 41}]];
Range[0, nn]! CoefficientList[Series[d[Exp[x] - 1 + x], {x, 0, nn}],x]
A369397
Number of binary relations R on [n] such that the (unique) idempotent in {R,R^2,R^3,...} is an equivalence relation.
Original entry on oeis.org
1, 1, 5, 157, 26345, 18218521, 47136254765, 451286947588597, 16264532016440908625, 2253156851039460378774961, 1219026648017155982267265596885, 2601923405098893502520360223043594957, 22040885615442635622424409144799379027505465
Offset: 0
- D. A. Gregory, S. Kirkland, and N. J. Pullman, Power convergent Boolean matrices, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117.
- S. Schwarz, On the semigroup of binary relations on a finite set , Czechoslovak Mathematical Journal, 1970.
Cf.
A366866 (binary relations R on [n] such that the (unique) idempotent in {R,R^2,R^3,...} is a quasiorder),
A365534,
A366218,
A365590,
A355612,
A365593,
A366252,
A366350,
A366218.
-
nn = 12; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
Length@# == 2 &][[All, 2]]; s[x_] := Total[strong Table[x^i/i!, {i, 1, 58}]];
Table[n!, {n, 0, nn}] CoefficientList[Series[Exp [s[2 x] - x], {x, 0, nn}], x]
Showing 1-3 of 3 results.
Comments