A000314 Number of mixed Husimi trees with n nodes; or labeled polygonal cacti with bridges.
1, 1, 1, 4, 31, 362, 5676, 111982, 2666392, 74433564, 2384579440, 86248530296, 3476794472064, 154579941792256, 7514932528712896, 396595845237540600, 22581060079942183936, 1379771773100463174608, 90059660791562688208128, 6253914166368448348512064
Offset: 0
Keywords
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..100
- G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory of graphs III, Proc. Nat. Acad. Sci. USA, 42 (1956), 529-535.
- Index entries for sequences related to cacti
- Index entries for sequences related to trees
Programs
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Maple
A:= proc(n) option remember; if n<=0 then x else convert(series(x* exp((2*A(n-1) -A(n-1)^2)/ (2-2*A(n-1))),x=0,n+2), polynom) fi end: a:= n-> if n=0 then 1 else coeff(series(A(n-1), x=0,n+1), x,n)*(n-1)! fi: seq(a(n), n=0..30); # Alois P. Heinz, Aug 20 2008
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Mathematica
A[n_] := A[n] = If[n <= 0, x, Normal[Series[x*Exp[(2*A[n-1]-A[n-1]^2)/ (2-2*A[n-1])], {x, 0, n+2}]]]; a[n_] := If[n == 0, 1, Coefficient [Series[A[n-1], {x, 0, n+1}], x, n]*(n-1)!]; Table [a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 03 2014, after Alois P. Heinz *)
Formula
a(n) = A035351/n, n>0. - Christian G. Bower, Nov 15 1998
Extensions
More terms from Christian G. Bower, Nov 15 1998