A070808 Sum(((-1)^k*binomial(4*n,k)),k=n..2*n).

1, 2, 42, 407, 6890, 88502, 1385727, 19762290, 303169770, 4514031830, 69135179542, 1050132147077, 16141218975167, 247800513084152, 3825796483371170, 59118992260132532, 916434202205565162

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = 1/2*(-1)^(2*n)*binomial(4*n, 2*n)+1/4*(-1)^n*binomial(4*n, n).

From Vaclav Kotesovec, Aug 04 2022: (Start)

Recurrence: 3*(n-1)*n*(2*n - 1)*(3*n - 2)*(3*n - 1)*(43*n^2 - 129*n + 96)*a(n) = 2*(n-1)*(4*n - 3)*(4*n - 1)*(473*n^4 - 1892*n^3 + 2561*n^2 - 1338*n + 216)*a(n-1) + 16*(2*n - 3)*(4*n - 7)*(4*n - 5)*(4*n - 3)*(4*n - 1)*(43*n^2 - 43*n + 10)*a(n-2).

a(n) ~ 2^(4*n - 3/2) / sqrt(Pi*n). (End)

Mathematica

Table[Sum[(-1)^k Binomial[4n, k], {k, n, 2n}], {n, 0, 20}] (* Harvey P. Dale, Nov 20 2014 *)

Crossrefs

Sequence in context: A066563 A202865 A360786 * A229474 A157056 A180425

Adjacent sequences: A070805 A070806 A070807 * A070809 A070810 A070811

Keyword

easy,nonn

Author

Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002

Status

approved