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 A014167 Partial sums of binary rooted tree numbers. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Index entries for sequences related to rooted trees FORMULA G.f.: (B(x)-x)/(x(1-x)) where B(x) is g.f. of A002572. EXAMPLE 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 + ... 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 *) CROSSREFS Cf. A002572. Sequence in context: A100671 A189600 A005251 * A103197 A307543 A255062 Adjacent sequences: A014164 A014165 A014166 * A014168 A014169 A014170 KEYWORD nonn AUTHOR N. J. A. Sloane. STATUS approved

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Last modified August 14 16:37 EDT 2024. Contains 375166 sequences. (Running on oeis4.)