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 A215982 Number of simple unlabeled graphs on n nodes with exactly 2 connected components that are trees or cycles. 3
 1, 1, 3, 5, 10, 17, 33, 62, 127, 267, 587, 1326, 3085, 7326, 17731, 43585, 108563, 273544, 696113, 1787042, 4623125, 12043071, 31565842, 83200763, 220413272, 586625403, 1567930743, 4207181144, 11329835687, 30613313339, 82975300030, 225552632043, 614787508640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 2..650 FORMULA a(n) ~ c * d^n / n^(5/2), where d = A051491 = 2.9557652856519949747148..., c = 0.3339525664158379... . - Vaclav Kotesovec, Sep 07 2014 EXAMPLE a(5) = 5: .o-o o.  .o-o o.  .o-o o.  .o o-o.  .o o-o.           .| |  .  .|    .  .|\   .  .|\   .  .|    .           .o-o  .  .o-o  .  .o o  .  .o-o  .  .o-o  . MAPLE with(numtheory): b:= proc(n) option remember; local d, j; `if` (n<=1, n,       (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))     end: g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-       (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2     end: p:= proc(n, i, t) option remember; `if`(n p(n, n, 2): seq(a(n), n=2..40); MATHEMATICA b[n_] := b[n] = If[n <= 1, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1)]; g[n_] := g[n] = If[n>2, 1, 0]+b[n]-(Sum [b[k]*b[n-k], {k, 0, n}] - If[Mod[n, 2] == 0, b[n/2], 0])/2; p[n_, i_, t_] := p[n, i, t] = If[n2 else 0) + b(n) - (sum([b(k)*b(n - k) for k in range(n + 1)]) - (b(n//2) if n%2==0 else 0))//2 @cacheit def p(n, i, t): return 0 if n

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Last modified July 1 09:41 EDT 2022. Contains 354958 sequences. (Running on oeis4.)