This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A014167 #21 Jul 08 2025 02:53:43
%S A014167 1,2,4,7,12,21,37,65,115,204,363,648,1158,2072,3711,6649,11918,21369,
%T A014167 38321,68731,123286,221157,396743,711759,1276927,2290903,4110101,
%U A014167 7373976,13229809,23735984,42585539,76404333,137080119,245941267,441254017,791673611
%N A014167 Partial sums of binary rooted tree numbers.
%H A014167 Alois P. Heinz, <a href="/A014167/b014167.txt">Table of n, a(n) for n = 1..1000</a>
%H A014167 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A014167 G.f.: (B(x)-x)/(x(1-x)) where B(x) is g.f. of A002572.
%e A014167 G.f. = x + 2*x^2 + 4*x^3 + 7*x^4 + 12*x^5 + 21*x^6 + 37*x^7 + 65*x^8 + 115*x^9 + ...
%p A014167 v:= proc(c,d) option remember; if d<0 or c<0 then 0 elif d=c then 1 else add(v(i,d-c), i=1..2*c) fi end: a:= proc(n) option remember; if n=0 then 0 else a(n-1) +v(1,n) fi end: seq(a(n), n=1..40); # _Alois P. Heinz_, Aug 22 2008
%t A014167 v[c_, d_] := v[c, d] = If[d<0 || c<0, 0, If[d == c, 1, Sum[v[i, d-c], {i, 1, 2c}]]]; a[n_] := a[n] = If[n == 0, 0, a[n-1]+v[1, n]]; Table[a[n], {n, 1, 29}] (* _Jean-François Alcover_, Mar 03 2014, after _Alois P. Heinz_ *)
%Y A014167 Cf. A002572.
%K A014167 nonn
%O A014167 1,2
%A A014167 _N. J. A. Sloane_