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

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..600

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

Maple

a:=n->sum((n-j)^j, j=2..n): seq(a(n), n=2..24); # Zerinvary Lajos, Jun 07 2008

Mathematica

Sum[(n - i)^(1 + i), {i, 1, n}]

Prog

(PARI) a(n) = sum(i=1, n, (n-i)^(1+i)); \\ Michel Marcus, Mar 24 2019

Crossrefs

Cf. A003101, A349878, A349879.

Sequence in context: A222567 A099449 A104630 * A350782 A255837 A122234

Adjacent sequences: A062806 A062807 A062808 * A062810 A062811 A062812

Keyword

nonn,easy

Author

Olivier Gérard, Jun 23 2001

Status

approved