A228002 Alternate partial sums of binomial(2n,n)^2.

1, 3, 33, 367, 4533, 58971, 794805, 10983819, 154653081, 2209251319, 31925528217, 465708778407, 6846750893929, 101325729466071, 1508015866093929, 22553429144856471, 338744206097695629, 5106973783924992771, 77251106929381097229, 1172036566162209342771

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..833

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

Cf. A115257, A188679, A188680.

Sequence in context: A080488 A342345 A082778 * A163476 A155660 A299507

Adjacent sequences: A227999 A228000 A228001 * A228003 A228004 A228005

Keyword

nonn,easy

Author

Vaclav Kotesovec, Aug 07 2013

Status

approved