Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Dec 19 2015 10:01:08
%S 1,5,14,33,72,149,301,599,1170,2254,4288,8081,15087,27971,51500,94293,
%T 171724,311328,562023,1010819,1811676,3236959,5766793,10246734,
%U 18162241,32119542,56682671,99833464,175509158,308014335,539675744,944115593,1649236884
%N Number of n-node rooted identity trees of height 6.
%C The number of terms with a(n)>0 is A038093(6) - 6. - _Alois P. Heinz_, Sep 22 2013
%H Alois P. Heinz, <a href="/A038090/b038090.txt">Table of n, a(n) for n = 7..1000</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038085 - A038084.
%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@@3)(f)-(wsh@@2)(f): seq(a(n), n=7..37); # _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[6]-PadRight[f[5],Length[f[6]]],6] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y Cf. A038081-A038093.
%Y Column k=6 of A227819.
%K nonn,fini
%O 7,2
%A _Christian G. Bower_, Jan 04 1999