Search: id:A000106
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%I A000106 M1415 N0553
%S A000106 1,2,5,12,30,74,188,478,1235,3214,8450,22370,59676,160140,432237,
%T A000106 1172436,3194870,8741442,24007045,66154654,182864692,506909562,
%U A000106 1408854940,3925075510,10959698606,30665337738,85967279447
%N A000106 2nd power of rooted tree enumerator; number of linear forests of 2 rooted 
               trees.
%D A000106 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000106 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000106 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               150.
%H A000106 T. D. Noe, <a href="b000106.txt">Table of n, a(n) for n=2..200</a>
%H A000106 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=385">
               Encyclopedia of Combinatorial Structures 385</a>
%H A000106 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A000106 Self-convolution of rooted trees A000081.
%p A000106 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-1)^2, x=0, n+1), x,n): seq 
               (a(n), n=2..28); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 21 2008]
%Y A000106 Cf. A000081, A000242, A000300, A000343, A000395.
%Y A000106 Sequence in context: A118649 A033482 A054341 this_sequence A076883 A140832 
               A026580
%Y A000106 Adjacent sequences: A000103 A000104 A000105 this_sequence A000107 A000108 
               A000109
%K A000106 nonn,nice,easy
%O A000106 2,2
%A A000106 N. J. A. Sloane (njas(AT)research.att.com).
%E A000106 More terms from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.

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