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.

1, 2, 8, 120, 40456, 14354709112, 10145806838546891496456, 43814454551364119293851205505402899467594454136, 12230705010706858303154182089533811056819321112988144670126813673854225371091425006635639297686024

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. A147780.

Programs

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 *)

Extensions

More terms from R. J. Mathar, May 04 2009