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 A274935 Number of n-node unlabeled forests with two connected components. 4
 1, 1, 2, 2, 4, 6, 12, 22, 46, 93, 205, 451, 1039, 2422, 5803, 14075, 34757, 86761, 219235, 558984, 1438033, 3726535, 9723913, 25525112, 67375200, 178723358, 476264352, 1274448596, 3423494617, 9229075121, 24961969420, 67721961268, 184255962564, 502658875034, 1374713691841, 3768527610094, 10353602341313 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS One of the components may be empty (the null graph): a(n) = A000055(n) + A274937(n). - R. J. Mathar, Aug 15 2017 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: [A(x)^2 + A(x^2)]/2 where A(x) is the o.g.f. for A000055. MAPLE with(numtheory): b:= proc(n) option remember; `if`(n<2, n, (add(add(d*       b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))     end: g:= proc(n) option remember; `if`(n=0, 1, b(n)-add(b(j)*       b(n-j), j=0..n/2)+`if`(n::odd, 0, (t->t*(t+1)/2)(b(n/2))))     end: a:= proc(n) option remember; add(g(j)*g(n-j), j=0..n/2)-       `if`(n::odd, 0, (t-> t*(t-1)/2)(g(n/2)))     end: seq(a(n), n=0..40);  # Alois P. Heinz, Jul 20 2016 MATHEMATICA b[n_] := b[n] = If[n<2, n, Sum[DivisorSum[j, #*b[#]&]*b[n-j], {j, 1, n-1}]/ (n-1)]; g[n_] := g[n] = If[n==0, 1, b[n]-Sum[b[j]*b[n-j], {j, 0, n/2}]+If[OddQ[n], 0, Function[t, t*(t+1)/2][b[n/2]]]]; a[n_] := a[n] = Sum[g[j]*g[n-j], {j, 0, n/2}]-If[OddQ[n], 0, Function[t, t*(t-1)/2][g[n/2]]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 15 2017, after Alois P. Heinz *) CROSSREFS Cf. A000055, A274936, A274937, A274938. [A274935, A274936, A274937, A274938] are analogs for forests of [A275165, A275166, A216785, A274934] for graphs. Sequence in context: A238014 A052953 A128209 * A188538 A282164 A268175 Adjacent sequences:  A274932 A274933 A274934 * A274936 A274937 A274938 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 19 2016 STATUS approved

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Last modified April 11 08:10 EDT 2021. Contains 342886 sequences. (Running on oeis4.)