A147780 Number of nodes at n-th level in tree in which top node is 1; each node k has children labeled 1, 2, ..., (k+1)^2 at next level.

1, 4, 54, 8422, 464862602, 7134230598346156958, 13246386641663595526163132113862494582602, 643152870463337226096381089442329605982736165294243832777767297119502149008481206286

Offset: 0

Author

N. J. A. Sloane, May 03 2009

Keywords

• nonn

Comments

See the reference in A058311 for a better way to compute this!

Crossrefs

A variant of A058311. Cf. A147794.

Programs

Maple

M:=3;
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+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)];
p := proc(n,k) option remember; local j ; if n = 1 then (k+1)^2; else sum( procname(n-1,j),j=1..(k+1)^2) ; fi; expand(%) ; end: A147780 := proc(n) if n = 0 then 1 ; else subs(k=1, p(n,k)) ; fi; end: for n from 0 do printf("%d,\n", A147780(n)) ; od: # R. J. Mathar, May 04 2009

Mathematica

p[n_, k_] := p[n, k] = If[n == 1, (k + 1)^2, Sum[p[n - 1, j], {j, 1, (k + 1)^2}]];
a[n_] := a[n] = If[n == 0, 1, p[n, 1]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 5}] (* Jean-François Alcover, Nov 28 2023, after R. J. Mathar *)

Extensions

4 more terms from R. J. Mathar, May 04 2009