A332779 Number of simple labeled graphs on n nodes with at most one nontrivial acyclic component.

1, 1, 2, 8, 61, 979, 32198, 2089277, 268307573, 68716923913, 35184302013572, 36028793426712833, 73786975811410580497, 302231454743896729891579, 2475880078460679602114069886, 40564819207152522033364153642067, 1329227995784508187140918633570844201

Offset

0,3

Links

Table of n, a(n) for n=0..16.

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

Cf. A000272, A001187.

Sequence in context: A191482 A140722 A327078 * A116976 A132574 A086903

Adjacent sequences: A332776 A332777 A332778 * A332780 A332781 A332782

Keyword

nonn

Author

Geoffrey Critzer, Feb 23 2020

Status

approved