|
|
A228002
|
|
Alternate partial sums of binomial(2n,n)^2.
|
|
3
|
|
|
1, 3, 33, 367, 4533, 58971, 794805, 10983819, 154653081, 2209251319, 31925528217, 465708778407, 6846750893929, 101325729466071, 1508015866093929, 22553429144856471, 338744206097695629, 5106973783924992771, 77251106929381097229, 1172036566162209342771
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Recurrence: n^2*a(n) = (3*n-2)*(5*n-2)*a(n-1) + 4*(2*n-1)^2*a(n-2).
a(n) ~ 16^(n+1)/(17*Pi*n).
|
|
MAPLE
|
series(2*EllipticK(4*x^(1/2))/(Pi*(1+x)), x=0, 20)
|
|
MATHEMATICA
|
Table[Sum[(-1)^(n-k)*Binomial[2*k, k]^2, {k, 0, n}], {n, 0, 20}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|