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.
1, 1, 5, 73, 2849, 277921, 65067905, 35545840513, 44384640206849, 124697899490480641, 778525887500557625345, 10693248499002776513697793, 320453350845793018626300755969, 20807125028666778079876193487790081, 2909872870574162514727072641529432735745
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..77
Programs
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Maple
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 -
Mathematica
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]
Formula
Sum_{n>=0} a_n*x^n/(n!*2^C(n,2)) = 1/(2-Sum_{n>=0} x^n/(n!*2^C(n,2))).
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