A014167 Partial sums of binary rooted tree numbers.

1, 2, 4, 7, 12, 21, 37, 65, 115, 204, 363, 648, 1158, 2072, 3711, 6649, 11918, 21369, 38321, 68731, 123286, 221157, 396743, 711759, 1276927, 2290903, 4110101, 7373976, 13229809, 23735984, 42585539, 76404333, 137080119, 245941267, 441254017, 791673611

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			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 + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A002572.

Programs

Maple

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

Mathematica

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 *)

Formula

G.f.: (B(x)-x)/(x(1-x)) where B(x) is g.f. of A002572.