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A339025 Sum of n-th powers of entries in the n-th row of Stern's triangle (A337277).

%I A339025 #11 May 30 2022 08:08:26
%S A339025 1,3,13,147,4277,314403,58215317,27104094867,31830051961045,
%T A339025 94398513955640643,709919097675516974293,13569078873978509433342387,
%U A339025 661668739571948876787281152277,82526665791586458931717457637364323,26412772665617176235336349304356162390677
%N A339025 Sum of n-th powers of entries in the n-th row of Stern's triangle (A337277).
%H A339025 Alois P. Heinz, <a href="/A339025/b339025.txt">Table of n, a(n) for n = 0..28</a>
%p A339025 b:= proc(n) option remember; `if`(n=0, 1, (h-> [1, h[1], seq(
%p A339025       [h[i-1]+h[i], h[i]][], i=2..nops(h)), 1][])([b(n-1)]))
%p A339025     end:
%p A339025 a:= proc(n) option remember; add(i^n, i=[b(n)]) end:
%p A339025 seq(a(n), n=0..15);
%t A339025 nmax = 15;
%t A339025 T = Nest[Append[#, Flatten@Join[{1}, If[Length@# > 1, Map[{#1, #1 + #2}& @@ #&, Partition[#[[-1]], 2, 1]], {}], {#[[-1, -1]]}, {1}]]&, {{1}}, nmax];
%t A339025 a[n_] := T[[n+1]]^n // Total;
%t A339025 Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, May 30 2022, after _Michael De Vlieger_ in A337277 *)
%Y A339025 Cf. A337277.
%K A339025 nonn
%O A339025 0,2
%A A339025 _Alois P. Heinz_, Nov 19 2020