cp's OEIS Frontend

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.

%I A147780 #9 Nov 28 2023 08:39:30
%S A147780 1,4,54,8422,464862602,7134230598346156958,
%T A147780 13246386641663595526163132113862494582602,
%U A147780 643152870463337226096381089442329605982736165294243832777767297119502149008481206286
%N 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.
%C A147780 See the reference in A058311 for a better way to compute this!
%p A147780 M:=3;
%p A147780 L[0]:=[1]; a[0]:=1;
%p A147780 for n from 1 to M do
%p A147780 L[n]:=[];
%p A147780 t1:=L[n-1];
%p A147780 tc:=nops(t1);
%p A147780 for i from 1 to tc do
%p A147780 t2:=t1[i];
%p A147780 for j from 1 to (t2+1)^2 do
%p A147780 L[n]:=[op(L[n]),j]; od:
%p A147780 a[n]:=nops(L[n]);
%p A147780 #lprint(n,L[n],a[n]);
%p A147780 od:
%p A147780 od:
%p A147780 [seq(a[n],n=0..M)];
%p A147780 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
%t A147780 p[n_, k_] := p[n, k] = If[n == 1, (k + 1)^2, Sum[p[n - 1, j], {j, 1, (k + 1)^2}]];
%t A147780 a[n_] := a[n] = If[n == 0, 1, p[n, 1]];
%t A147780 Table[Print[n, " ", a[n]]; a[n], {n, 0, 5}] (* _Jean-François Alcover_, Nov 28 2023, after _R. J. Mathar_ *)
%Y A147780 A variant of A058311. Cf. A147794.
%K A147780 nonn
%O A147780 0,2
%A A147780 _N. J. A. Sloane_, May 03 2009
%E A147780 4 more terms from _R. J. Mathar_, May 04 2009