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

1, 3, 8, 23, 73, 251, 920, 3573, 14695, 64047, 295792, 1445659, 7460349, 40539363, 231303192, 1381924345, 8623569739, 56078184471, 379232618512, 2662012084719, 19362915524849, 145719545817995, 1133022996552664, 9090156893772893, 75161929706243087, 639793220810832639

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..590

Programs

Magma

A047857:= func< n | n+1 + (&+[((k+1)^(n-k+2) -1)/k: k in [2..n+2]]) >;
[A047857(n): n in [0..30]]; // G. C. Greubel, Jan 17 2025

Mathematica

Table[Sum[((k+3)^(n-k) +k+1)/(k+2), {k,0,n}], {n,0,25}] (* Vaclav Kotesovec, May 23 2021 *)

Python

def A047857(n): return n+1 +sum((pow(k+1, n-k+2) -1)//k for k in range(2,n+3))
print([A047857(n) for n in range(31)]) # G. C. Greubel, Jan 17 2025

Formula

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

Extensions

a(14) onward corrected by Sean A. Irvine, May 22 2021

More terms from G. C. Greubel, Jan 17 2025