cp's OEIS Frontend

A000314 Number of mixed Husimi trees with n nodes; or labeled polygonal cacti with bridges.

%I A000314 M3639 N1480 #30 Dec 29 2014 17:29:42
%S A000314 1,1,1,4,31,362,5676,111982,2666392,74433564,2384579440,86248530296,
%T A000314 3476794472064,154579941792256,7514932528712896,396595845237540600,
%U A000314 22581060079942183936,1379771773100463174608,90059660791562688208128,6253914166368448348512064
%N A000314 Number of mixed Husimi trees with n nodes; or labeled polygonal cacti with bridges.
%D A000314 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000314 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000314 Alois P. Heinz, <a href="/A000314/b000314.txt">Table of n, a(n) for n = 0..100</a>
%H A000314 G. W. Ford and G. E. Uhlenbeck, <a href="http://www.jstor.org/stable/89494">Combinatorial problems in the theory of graphs III</a>, Proc. Nat. Acad. Sci. USA, 42 (1956), 529-535.
%H A000314 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%H A000314 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A000314 a(n) = A035351/n, n>0. - _Christian G. Bower_, Nov 15 1998
%p A000314 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
%t A000314 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_ *)
%Y A000314 Cf. A000083, A000237, A035082, A035349-A035357.
%K A000314 nonn
%O A000314 0,4
%A A000314 _N. J. A. Sloane_
%E A000314 More terms from _Christian G. Bower_, Nov 15 1998