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%I #24 Aug 25 2017 07:18:28
%S 1,3,5,8,12,17,23,32,41,52,66,83,102,124,152,181,216,255,299,346,400,
%T 458,521,588,659,735,814,896,979,1067,1151,1239,1324,1407,1486,1564,
%U 1635,1700,1759,1809,1853,1887,1912,1925,1932,1925,1912,1887,1853
%N Number of n-node rooted identity trees of height 4.
%H Alois P. Heinz, <a href="/A038088/b038088.txt">Table of n, a(n) for n = 5..97</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = A038083(n) - A038082(n).
%p weigh:= proc(p) proc(n) local x, k; coeff(series(mul((1+x^k)^p(k), k=1..n), x, n+1), x, n) end end: wsh:= p-> n-> weigh(p)(n-1): f:= n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0): a:= wsh(f)-f: seq(a(n), n=5..97); # _Alois P. Heinz_, Sep 10 2008
%t f[n_]:=Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]],{i,1,Length[#]}],{x,0,50}],x]&,{1},n];Drop[f[4]-PadRight[f[3],Length[f[4]]],4] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y Cf. A038081-A038093.
%Y Column k=4 of A227819.
%K nonn,fini,full
%O 5,2
%A _Christian G. Bower_, Jan 04 1999
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