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

1, 3, 13, 147, 4277, 314403, 58215317, 27104094867, 31830051961045, 94398513955640643, 709919097675516974293, 13569078873978509433342387, 661668739571948876787281152277, 82526665791586458931717457637364323, 26412772665617176235336349304356162390677

Offset: 0

Author

Alois P. Heinz, Nov 19 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..28

Crossrefs

Cf. A337277.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, (h-> [1, h[1], seq(
      [h[i-1]+h[i], h[i]][], i=2..nops(h)), 1][])([b(n-1)]))
    end:
a:= proc(n) option remember; add(i^n, i=[b(n)]) end:
seq(a(n), n=0..15);

Mathematica

nmax = 15;
T = Nest[Append[#, Flatten@Join[{1}, If[Length@# > 1, Map[{#1, #1 + #2}& @@ #&, Partition[#[[-1]], 2, 1]], {}], {#[[-1, -1]]}, {1}]]&, {{1}}, nmax];
a[n_] := T[[n+1]]^n // Total;
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, May 30 2022, after Michael De Vlieger in A337277 *)