A374601 Defined by: Sum_{i=1..n} i*a(i)/n^i = 1, n>=1.
1, 1, 4, 28, 278, 3554, 55382, 1015750, 21401830, 508932130, 13475090126, 393026736854, 12518884854734, 432357148756210, 16092438499462630, 642170913160160710, 27351173629037613494, 1238472705706192189442, 59411223892666111129022, 3010044856761072109710262
Offset: 1
Keywords
Examples
1*a(1)/1^1 = 1, so a(1) = 1. 1*a(1)/2^1 + 2*a(2)/2^2 = 1, so a(2) = 1. 1*a(1)/3^1 + 2*a(2)/3^2 + 3*a(3)/3^3 = 1, so a(3) = 4.
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..387
Crossrefs
Cf. A374562.
Programs
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Maple
a:= proc(n) option remember; `if`(n<1, 0, n^(n-1)-add(n^(n-1-i)*a(i)*i, i=1..n-1)) end: seq(a(n), n=1..20); # Alois P. Heinz, Jul 13 2024 -
Mathematica
a[n_]:=a[n]=n^(n-1)-Sum[n^(n-1-i)*i*a[i],{i,1,n-1}] -
PARI
a(n)=n^(n-1)-sum(i=1,n-1,n^(n-1-i)*i*a(i))
Formula
a(n) = n^(n-1) - Sum_{i=1..n-1} n^(n-1-i)*i*a(i).
a(n) = A374562(n)/n.