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A332779
Number of simple labeled graphs on n nodes with at most one nontrivial acyclic component.
0
1, 1, 2, 8, 61, 979, 32198, 2089277, 268307573, 68716923913, 35184302013572, 36028793426712833, 73786975811410580497, 302231454743896729891579, 2475880078460679602114069886, 40564819207152522033364153642067, 1329227995784508187140918633570844201
OFFSET
0,3
FORMULA
E.g.f.: exp(x)*exp(c(x) - t(x) )*(t(x) - x) where c(x) is the e.g.f. for A001187 and t(x) is the e.g.f. for A000272.
MATHEMATICA
nn = 16; f[x_] := Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; a =
Range[0, nn]! CoefficientList[Series[ 1 + Log[f[x]], {x, 0, nn}], x];
c[x_] := Sum[a[[i]] x^(i - 1)/(i - 1)!, {i, 1, nn + 1}];
t[x_] := 1 + Sum[n^(n - 2) x^n/n!, {n, 1, nn}];
Range[0, nn]! CoefficientList[Series[Exp[x] Exp[c[x] - t[x]] (t[x] - x), {x, 0, nn}], x]
CROSSREFS
Sequence in context: A191482 A140722 A327078 * A116976 A132574 A086903
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Feb 23 2020
STATUS
approved