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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.
0
-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.
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
Sequence in context: A304859 A303292 A010332 * A198258 A200819 A232146
KEYWORD
sign,frac
AUTHOR
Mats Granvik, Dec 31 2023
STATUS
approved