|
|
A347994
|
|
a(n) = n! * Sum_{k=1..n-1} (-1)^(k+1) * n^(n-k-2) / (n-k-1)!.
|
|
1
|
|
|
0, 1, 4, 30, 296, 3720, 56652, 1014832, 20909520, 487198080, 12667470740, 363607605504, 11420819358456, 389646915374080, 14349217119054300, 567315485527234560, 23967624180805666208, 1077568488585047605248, 51369752823292604784420, 2588268388538639982592000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: -LambertW(-x) - log(1 - LambertW(-x)).
|
|
MATHEMATICA
|
Table[n! Sum[(-1)^(k + 1) n^(n - k - 2)/(n - k - 1)!, {k, 1, n - 1}], {n, 1, 20}]
nmax = 20; CoefficientList[Series[-LambertW[-x] - Log[1 - LambertW[-x]], {x, 0, nmax}], x] Range[0, nmax]! // Rest
|
|
PROG
|
(PARI) a(n) = n! * sum(k=1, n-1, (-1)^(k+1)*n^(n-k-2)/(n-k-1)!); \\ Michel Marcus, Sep 23 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|