cp's OEIS Frontend

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.

%I A147794 #8 Feb 01 2024 15:00:00
%S A147794 1,2,8,120,40456,14354709112,10145806838546891496456,
%T A147794 43814454551364119293851205505402899467594454136,
%U A147794 12230705010706858303154182089533811056819321112988144670126813673854225371091425006635639297686024
%N 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.
%C A147794 See the reference in A058311 for a better way to compute this!
%p A147794 M:=4;
%p A147794 L[0]:=[1]; a[0]:=1;
%p A147794 for n from 1 to M do
%p A147794 L[n]:=[];
%p A147794 t1:=L[n-1];
%p A147794 tc:=nops(t1);
%p A147794 for i from 1 to tc do
%p A147794 t2:=t1[i];
%p A147794 for j from 1 to t2*(t2+1) do
%p A147794 L[n]:=[op(L[n]),j]; od:
%p A147794 a[n]:=nops(L[n]);
%p A147794 #lprint(n,L[n],a[n]);
%p A147794 od:
%p A147794 od:
%p A147794 [seq(a[n],n=0..M)];
%p A147794 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 A147794 p[n_, k_] := p[n, k] = If[n == 1, k (k + 1), Sum[p[n - 1, j], {j, 1, k (k + 1)}]];
%t A147794 a[n_] := If[n == 0, 1, p[n, 1]];
%t A147794 Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* _Jean-François Alcover_, Feb 01 2024, after _R. J. Mathar_ *)
%Y A147794 A variant of A058311. Cf. A147780.
%K A147794 nonn
%O A147794 0,2
%A A147794 _N. J. A. Sloane_, May 03 2009
%E A147794 More terms from _R. J. Mathar_, May 04 2009