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A047857 a(n) = Sum_{k=0..n} A047848(k, n-k).

%I A047857 #18 Jan 18 2025 03:11:48
%S A047857 1,3,8,23,73,251,920,3573,14695,64047,295792,1445659,7460349,40539363,
%T A047857 231303192,1381924345,8623569739,56078184471,379232618512,
%U A047857 2662012084719,19362915524849,145719545817995,1133022996552664,9090156893772893,75161929706243087,639793220810832639
%N A047857 a(n) = Sum_{k=0..n} A047848(k, n-k).
%H A047857 G. C. Greubel, <a href="/A047857/b047857.txt">Table of n, a(n) for n = 0..590</a>
%F A047857 a(n) = n + 2 - H(n+2) + Sum_{k=2..n+2} (k+1)^(n-k+2)/k, where H(n) is the nth Harmonic number. - _G. C. Greubel_, Jan 17 2025
%t A047857 Table[Sum[((k+3)^(n-k) +k+1)/(k+2), {k,0,n}], {n,0,25}] (* _Vaclav Kotesovec_, May 23 2021 *)
%o A047857 (Magma)
%o A047857 A047857:= func< n | n+1 + (&+[((k+1)^(n-k+2) -1)/k: k in [2..n+2]]) >;
%o A047857 [A047857(n): n in [0..30]]; // _G. C. Greubel_, Jan 17 2025
%o A047857 (Python)
%o A047857 def A047857(n): return n+1 +sum((pow(k+1, n-k+2) -1)//k for k in range(2,n+3))
%o A047857 print([A047857(n) for n in range(31)]) # _G. C. Greubel_, Jan 17 2025
%K A047857 nonn
%O A047857 0,2
%A A047857 _Clark Kimberling_
%E A047857 a(14) onward corrected by _Sean A. Irvine_, May 22 2021
%E A047857 More terms from _G. C. Greubel_, Jan 17 2025