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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
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
Vaclav Kotesovec, Aug 07 2013
STATUS
approved