|
|
A362350
|
|
a(n) = n! * Sum_{k=0..floor(n/2)} (k/2)^k / (k! * (n-2*k)!).
|
|
5
|
|
|
1, 1, 2, 4, 19, 71, 601, 3277, 39089, 277489, 4250341, 37110701, 693581197, 7184750509, 158461520309, 1899055549861, 48269252293201, 656869268651537, 18903165795857089, 287927838327392929, 9252988524143245181, 155954097639111859501
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: exp(x) / (1 + LambertW(-x^2/2)).
a(n) ~ (exp(2^(3/2)*exp(-1/2)) + (-1)^n) * n^n / (2^((n+1)/2) * exp(n/2 + sqrt(2)*exp(-1/2))). - Vaclav Kotesovec, Apr 18 2023
|
|
PROG
|
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2/2))))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|