A000314 Number of mixed Husimi trees with n nodes; or labeled polygonal cacti with bridges. (Formerly M3639 N1480)

1, 1, 1, 4, 31, 362, 5676, 111982, 2666392, 74433564, 2384579440, 86248530296, 3476794472064, 154579941792256, 7514932528712896, 396595845237540600, 22581060079942183936, 1379771773100463174608, 90059660791562688208128, 6253914166368448348512064

Offset

0,4

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

Formula

a(n) = A035351/n, n>0. - Christian G. Bower, Nov 15 1998

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

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 *)

Crossrefs

Cf. A000083, A000237, A035082, A035349-A035357.

Sequence in context: A368237 A016036 A322626 * A128709 A138860 A266757

Adjacent sequences: A000311 A000312 A000313 * A000315 A000316 A000317

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower, Nov 15 1998

Status

approved