A368592 a(n) = numerator of -(1/4)*n!*(2 + n!)*(-2 + 1/(1 + floor(n/2 - 1/2))) - n!*Sum_{m=1..1 + 2*floor(n/2 - 1/2)} 1/m.

-1, 0, 7, 190, 5826, 214956, 11104542, 711175536, 59256152496, 5925678248160, 730285755406560, 105161159860398720, 18003044434808914560, 3528596711774282883840, 801568243461355261718400, 205201470326854119387494400, 59742508072063053997776844800

Offset

1,3

Comments

In the sum formula below, changing n! to n in the outer summation yields A161664.

Links

Table of n, a(n) for n=1..17.

Formula

For n>1: a(n) = Sum_{h=1..n!} Sum_{m=1..1 + 2*floor(n/2 - 1/2)} Sum_{k=1 + floor(h/(m + 1))..floor(h/m - 1/m)} 1.

Example

The fractions, of which a(n) is the numerator, begin: -1/4, 0, 7, 190, 5826, ...

Mathematica

Numerator[Table[-1/4*n!*(2 + n!)*(-2 + 1/(1 + Floor[n/2 - 1/2])) - n!*Sum[1/m, {m, 1, 1 + 2*Floor[n/2 - 1/2]}], {n, 1, 17}]]

Crossrefs

Cf. A161664, A006218.

Sequence in context: A304859 A303292 A010332 * A198258 A200819 A232146

Adjacent sequences: A368589 A368590 A368591 * A368593 A368594 A368595

Keyword

sign,frac

Author

Mats Granvik, Dec 31 2023

Status

approved