|
| |
|
|
A360934
|
|
Expansion of e.g.f. Sum_{k>=0} exp((4^k - 1)*x) * x^k/k!.
|
|
2
|
|
|
|
1, 1, 7, 73, 1711, 75121, 6743287, 1169659513, 412296162271, 284887781497441, 400134611520973927, 1108533158650520901673, 6238465090832886119430031, 69421876683500992783472318161, 1567475216919199483376363835235927
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f.: Sum_{k>=0} x^k/(1 - (4^k - 1)*x)^(k+1).
a(n) = Sum_{k=0..n} (4^k - 1)^(n-k) * binomial(n,k).
|
|
|
PROG
|
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp((4^k-1)*x)*x^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(4^k-1)*x)^(k+1)))
(PARI) a(n) = sum(k=0, n, (4^k-1)^(n-k)*binomial(n, k));
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
