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 A274936 Number of n-node unlabeled forests that have 2 non-isomorphic components. 4
 0, 1, 1, 2, 3, 6, 11, 22, 44, 93, 202, 451, 1033, 2422, 5792, 14075, 34734, 86761, 219188, 558984, 1437927, 3726535, 9723678, 25525112, 67374649, 178723358, 476263051, 1274448596, 3423491458, 9229075121, 24961961679, 67721961268, 184255943244, 502658875034, 1374713643212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. a(2n+1) = A274935(2n+1). a(2n) = A274935(2n)-A000055(n). - R. J. Mathar, Jul 20 2016 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, A274935-A274938. [A274935, A274936, A274937, A274938] are analogs for forests of [A275165, A275166, A216785, A274934] for graphs. Sequence in context: A132831 A354208 A007477 * A244521 A096202 A036653 Adjacent sequences: A274933 A274934 A274935 * A274937 A274938 A274939 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 19 2016 STATUS approved

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Last modified May 28 01:31 EDT 2023. Contains 362992 sequences. (Running on oeis4.)