A062809 a(n) = Sum_{i = 1..n} (n - i)^(1 + i).
0, 1, 5, 18, 60, 203, 725, 2772, 11368, 49853, 232757, 1151902, 6018772, 33087191, 190780197, 1150653904, 7241710912, 47454745785, 323154696165, 2282779990474, 16700904488684, 126356632390275, 987303454928949
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..600
Programs
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Maple
a:=n->sum((n-j)^j,j=2..n): seq(a(n), n=2..24); # Zerinvary Lajos, Jun 07 2008
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Mathematica
Sum[(n - i)^(1 + i), {i, 1, n}] -
PARI
a(n) = sum(i=1, n, (n-i)^(1+i)); \\ Michel Marcus, Mar 24 2019
Formula
a(n) ~ sqrt(2*Pi) * ((n + 1)/LambertW(exp(1)*(n + 1)))^(1/2 + (n + 1)*(1 - 1/LambertW(exp(1)*(n + 1)))) / sqrt(1 + LambertW(exp(1)*(n + 1))). - Vaclav Kotesovec, Dec 04 2021