|
|
A372333
|
|
Expansion of e.g.f. -exp(x) * LambertW(-2*x)/2.
|
|
2
|
|
|
0, 1, 6, 51, 684, 12965, 317298, 9500631, 336237016, 13729172553, 635237632350, 32844916975739, 1876755685038468, 117437155609780461, 7986793018367861194, 586578825469711599135, 46268265552518066488752, 3901008402618593931019409
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=1..n} (2*k)^(k-1) * binomial(n,k).
G.f.: Sum_{k>=1} (2*k)^(k-1) * x^k / (1-x)^(k+1).
|
|
PROG
|
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-exp(x)*lambertw(-2*x)/2)))
(PARI) a(n) = sum(k=1, n, (2*k)^(k-1)*binomial(n, k));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|