|
|
A098481
|
|
Expansion of 1/sqrt((1-x)^2 - 12*x^3).
|
|
4
|
|
|
1, 1, 1, 7, 19, 37, 115, 361, 937, 2599, 7777, 22195, 62701, 182647, 531829, 1534903, 4461571, 13034917, 38015899, 110994193, 325011151, 952442557, 2792471239, 8198275933, 24093817531, 70852613041, 208516575043, 614145137137
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
1/sqrt((1-x)^2 - 4*r*x^3) expands to Sum_{k=0..floor(n/2)} binomial(n-k, k)*binomial(n-2k, k)*r^k.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*binomial(n-2k, k)*3^k.
D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) + 6*(2*n-3)*a(n-3). - Vaclav Kotesovec, Jun 23 2014
|
|
MATHEMATICA
|
CoefficientList[Series[1/Sqrt[(1-x)^2-12x^3], {x, 0, 40}], x] (* Harvey P. Dale, Jun 02 2011 *)
|
|
PROG
|
(PARI) Vec(1/sqrt((1-x)^2 - 12*x^3) + O(x^50)) \\ G. C. Greubel, Jan 30 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|