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A147794 Number of nodes at n-th level in tree in which top node is 1; each node k has children labeled 1, 2, ..., k*(k+1) at next level. 3
1, 2, 8, 120, 40456, 14354709112, 10145806838546891496456, 43814454551364119293851205505402899467594454136, 12230705010706858303154182089533811056819321112988144670126813673854225371091425006635639297686024 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
See the reference in A058311 for a better way to compute this!
LINKS
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 1 to t2*(t2+1) 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)];
p := proc(n, k) option remember; local j ; if n = 1 then k*(k+1); else sum( procname(n-1, j), j=1..k*(k+1)) ; fi; expand(%) ; end: A147794 := proc(n) if n = 0 then 1 ; else subs(k=1, p(n, k)) ; fi; end: for n from 0 do printf("%d, \n", A147794(n)) ; od: # R. J. Mathar, May 04 2009
MATHEMATICA
p[n_, k_] := p[n, k] = If[n == 1, k (k + 1), Sum[p[n - 1, j], {j, 1, k (k + 1)}]];
a[n_] := If[n == 0, 1, p[n, 1]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* Jean-François Alcover, Feb 01 2024, after R. J. Mathar *)
CROSSREFS
A variant of A058311. Cf. A147780.
Sequence in context: A064111 A112094 A009658 * A358152 A027530 A228064
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 03 2009
EXTENSIONS
More terms from R. J. Mathar, May 04 2009
STATUS
approved

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Last modified May 21 12:09 EDT 2024. Contains 372736 sequences. (Running on oeis4.)