Search: id:A000343
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%I A000343 M3901 N1601
%S A000343 1,5,20,70,230,721,2200,6575,19385,56575,163952,472645,1357550,
%T A000343 3888820,11119325,31753269,90603650,258401245,736796675,2100818555,
%U A000343 5990757124,17087376630,48753542665,139155765455,397356692275
%N A000343 5th power of rooted tree enumerator; number of linear forests of 5 rooted 
               trees.
%D A000343 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000343 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000343 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               150.
%H A000343 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A000343 G.f.: B(x)^5 where B(x) is g.f. of A000081.
%p A000343 b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), 
               k=1..n-1)/(n-1) fi end: s:= proc(n,k) option remember; add(b(n+1-j*k), 
               j=1..iquo(n,k)) end: B:= proc(n) option remember; add (b(k)*x^k, 
               k=1..n) end: a:= n-> coeff (series (B(n-4)^5, x=0, n+1), x,n): seq 
               (a(n), n=5..29); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 21 2008]
%Y A000343 Cf. A000081, A000106, A000242, A000300, A000395.
%Y A000343 Sequence in context: A055403 A089094 A080930 this_sequence A005324 A154638 
               A054889
%Y A000343 Adjacent sequences: A000340 A000341 A000342 this_sequence A000344 A000345 
               A000346
%K A000343 nonn
%O A000343 5,2
%A A000343 N. J. A. Sloane (njas(AT)research.att.com).
%E A000343 More terms from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.

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