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%I #8 Feb 01 2024 15:00:00
%S 1,2,8,120,40456,14354709112,10145806838546891496456,
%T 43814454551364119293851205505402899467594454136,
%U 12230705010706858303154182089533811056819321112988144670126813673854225371091425006635639297686024
%N 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.
%C See the reference in A058311 for a better way to compute this!
%p M:=4;
%p L[0]:=[1]; a[0]:=1;
%p for n from 1 to M do
%p L[n]:=[];
%p t1:=L[n-1];
%p tc:=nops(t1);
%p for i from 1 to tc do
%p t2:=t1[i];
%p for j from 1 to t2*(t2+1) do
%p L[n]:=[op(L[n]),j]; od:
%p a[n]:=nops(L[n]);
%p #lprint(n,L[n],a[n]);
%p od:
%p od:
%p [seq(a[n],n=0..M)];
%p 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
%t p[n_, k_] := p[n, k] = If[n == 1, k (k + 1), Sum[p[n - 1, j], {j, 1, k (k + 1)}]];
%t a[n_] := If[n == 0, 1, p[n, 1]];
%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* _Jean-François Alcover_, Feb 01 2024, after _R. J. Mathar_ *)
%Y A variant of A058311. Cf. A147780.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 03 2009
%E More terms from _R. J. Mathar_, May 04 2009
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