Ugly But Interesting Harmonic Number Sequence

[Leroy Quet]

Let H(n) = sum{k=1 to n} 1/k, the nth harmonic number.
(H(0) = 0.)

Then, for n = any *positive* integer,

a(n) = ( (2n)!*(1 -H(2n))/2 + (2n+1)!*(H(n+1)/(n+2) - H(2n+2)/(2n+3)) 
)/(n+1)

is always an integer.


I based this result on an identity I found years ago which I cannot 
remember how I got it. So perhaps the above result is wrong.

But my question to seq.fan is, is it appropriate to submit unaestheticly 
generated integer sequences which are interesting solely because every 
term is an integer?

And if so, and if each a(n) is an integer, could someone please calculate 
and submit the sequence {a(k)}?

Thanks,
Leroy Quet