

A058311


Number of nodes at nth 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
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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 seq is wellknown, eg 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[n1];
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(k1) else sum( procname(n1, 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


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



