A038157 -id:A038157 - cp's OEIS frontend

A038158 a(n) = (n!/2)*Sum(1/k!, k=1..n-2).

0, 0, 0, 3, 18, 100, 615, 4326, 34636, 311760, 3117645, 34294150, 411529866, 5349888336, 74898436795, 1123476552030, 17975624832600, 305585622154336, 5500541198778201, 104510282776785990, 2090205655535719990, 43894318766250120000

Offset: 0

N. J. A. Sloane

nonn

G. A. Kamel, Partial Chain Topologies on Finite Sets, Computational and Applied Mathematics Journal. Vol. 1, No. 4, 2015, pp. 174-179.

Row sums of A268217.

Cf. A038157.

a(n) = (n!/2)*sum(k=1, n-2, 1/k!); \\ Michel Marcus, Jan 30 2016

a(n) = A038157(n) / 2. - Sean A. Irvine, Jan 09 2021

A082459 Multiply by 1, add 1, multiply by 2, add 2, etc.

Original entry on oeis.org

-1, -1, 0, 0, 2, 6, 9, 36, 40, 200, 205, 1230, 1236, 8652, 8659, 69272, 69280, 623520, 623529, 6235290, 6235300, 68588300, 68588311, 823059732, 823059744, 10699776672, 10699776685, 149796873590, 149796873604, 2246953104060, 2246953104075, 35951249665200, 35951249665216

Offset: 0

Vladeta Jovovic, Apr 25 2003

sign

Bisections: A038156 and A038157.

Robert Israel, Table of n, a(n) for n = 0..898

Cf. A019464 - A019466.

seq(op(simplify([exp(1)*GAMMA(k+1,1)-k!-1, exp(1)*GAMMA(k+2,1)-(k+1)!-k-2])),k=0..20); # Robert Israel, Jan 11 2018

FoldList[If[OddQ@ #2, #1 ((#2 + 1)/2), #1 + #2/2] &, -1, Range@ 31] (* Michael De Vlieger, Jan 11 2018 *)

From Robert Israel, Jan 11 2018: (Start)
a(2*k) = e*Gamma(k+1,1) - k! - 1.
a(2*k+1) = e*Gamma(k+2,1) - (k+1)! - k - 2. (End)

cp's OEIS Frontend

A038158 a(n) = (n!/2)*Sum(1/k!, k=1..n-2).

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