|
|
A374497
|
|
Expansion of 1/(1 - 4*x - 4*x^2)^(3/2).
|
|
2
|
|
|
1, 6, 36, 200, 1080, 5712, 29792, 153792, 787680, 4009280, 20304768, 102405888, 514678528, 2579028480, 12890311680, 64283809792, 319954540032, 1589720712192, 7886437652480, 39069462835200, 193307835764736, 955361266917376, 4716674314223616, 23264437702656000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(0) = 1, a(1) = 6; a(n) = (2*(2*n+1)*a(n-1) + 4*(n+1)*a(n-2))/n.
a(n) = binomial(n+2,2) * A071356(n).
|
|
PROG
|
(PARI) a(n) = binomial(n+2, 2)*sum(k=0, n\2, 2^(n-k)*binomial(n, 2*k)*binomial(2*k, k)/(k+1));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|