Search: id:A000314
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%I A000314 M3639 N1480
%S A000314 1,1,1,4,31,362,5676,111982,2666392,74433564,2384579440,86248530296,
%T A000314 3476794472064,154579941792256,7514932528712896,396595845237540600
%N A000314 Number of mixed Husimi trees with n nodes; or labeled polygonal cacti 
               with bridges.
%D A000314 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000314 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000314 G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory 
               of graphs III, Proc. Nat. Acad. Sci. USA, 42 (1956), 529-535.
%H A000314 Alois P. Heinz, <a href="b000314.txt">Table of n, a(n) for n = 0..100</
               a>
%H A000314 <a href="Sindx_Ca.html#cacti">Index entries for sequences related to 
               cacti</a>
%H A000314 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000314 A035351/n, n>0.
%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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 20 2008]
%Y A000314 Cf. A000083, A000237, A035082, A035349-A035357.
%Y A000314 Sequence in context: A145561 A086677 A016036 this_sequence A128709 A138860 
               A145087
%Y A000314 Adjacent sequences: A000311 A000312 A000313 this_sequence A000315 A000316 
               A000317
%K A000314 nonn
%O A000314 0,4
%A A000314 N. J. A. Sloane (njas(AT)research.att.com).
%E A000314 More terms and formula from Christian G. Bower (bowerc(AT)usa.net), Nov 
               15 1998

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