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 A058311 Number of nodes at n-th level in tree in which top node is 1; each node k has children labeled k, k+1, ..., (k+1)^2 at next level. 3
 1, 4, 48, 7918, 463339346, 7134188685100826388, 13246386641449904934758023373599438217628, 643152870463337226096320122089499144560533929707886143570111588898313745804013188842 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Triggered by a comment from Michael Kleber, Dec 08 2009, who said: The algorithm in my paper with Cook lets you compute the equivalent sequence where the children of a node labeled (k) are labeled with all the integers in the interval [p(k), q(k)] where p,q are any polynomials you like (in the paper, p(k)=k+1 and q(k)=2k). For a bunch of p,q the resulting sequence is well known, e.g., p(k)=1, q(k)=k+1 is the Catalan numbers. LINKS Table of n, a(n) for n=0..7. M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44. MAPLE M:=4; L[0]:=[1]; a[0]:=1; for n from 1 to M do L[n]:=[]; t1:=L[n-1]; tc:=nops(t1); for i from 1 to tc do t2:=t1[i]; for j from t2 to (t2+1)^2 do L[n]:=[op(L[n]), j]; od: a[n]:=nops(L[n]); #lprint(n, L[n], a[n]); od: od: [seq(a[n], n=0..M)]; # See the reference for a better way to compute this! p := proc(n, k) option remember; local j ; if n = 1 then k^2+k+2; # (k+1)^2-(k-1) else sum( procname(n-1, j), j=k..(k+1)^2) ; fi; expand(%) ; end proc: A058311 := proc(n) if n = 0 then 1 ; else subs(k=1, p(n, k)) ; fi; end proc: for n from 0 do printf("%d, \n", A058311(n)) ; od: # R. J. Mathar, May 04 2009 MATHEMATICA p[n_, k_] := p[n, k] = If[n == 1, k^2+k+2, Sum[p[n-1, j], {j, k, (k+1)^2}]]; a[n_] := If[n == 0, 1, p[n, 1]]; Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* Jean-François Alcover, Jun 26 2023, after R. J. Mathar *) CROSSREFS Cf. A008934, A058222, A147780, A147794. Sequence in context: A123373 A264265 A132510 * A189347 A248558 A198384 Adjacent sequences: A058308 A058309 A058310 * A058312 A058313 A058314 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 09 2000 EXTENSIONS Corrected, with Maple program, by N. J. A. Sloane, May 03 2009. Thanks to Max Alekseyev for pointing out that something was wrong. Replaced a(4), added three more terms - R. J. Mathar, May 04 2009 STATUS approved

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Last modified September 26 00:10 EDT 2023. Contains 365649 sequences. (Running on oeis4.)