|
|
A372334
|
|
Expansion of e.g.f. -exp(x) * LambertW(-3*x)/3.
|
|
2
|
|
|
0, 1, 8, 102, 2092, 60140, 2220954, 100119670, 5328468968, 326960686872, 22724388453070, 1764411577328906, 151364204180518476, 14217940294767407380, 1451334877597451677250, 159972528561402504191190, 18936257811933773637390544, 2395818853376147403857700656
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=1..n} (3*k)^(k-1) * binomial(n,k).
G.f.: Sum_{k>=1} (3*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(-3*x)/3)))
(PARI) a(n) = sum(k=1, n, (3*k)^(k-1)*binomial(n, k));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|