Problems with xrefs to A127585

[Jonathan Post]

Thank you Frank.

Now I can, unless you object, submit a sequence correctly
crossreferencing my A127585, along these lines:

Error term in Stirling's approximation truncated after e^(-n).

a(n) = Floor[(sqrt(2*pi))*(n^(n+(1/2)))*(e^(-n))]

offset 1,5

0, 0, 0, 0, 1, 9, 59, 417, 3343, 30104, 301174, 3314113, 39781324

a(14) ~ 517289459 but these were crudely calculated with the Google
calculator.  Before I submit, Frank, are these correct, as done with a
higher precision program?

example:

a(7) = Floor[(sqrt(2*pi))*(7^(7+(1/2)))*(e^(-7))]
= Floor[59.6041684] = 59.

Citation to equation (17)  in Weisstein reference "Stirling's
approximation" in MathWorld.

Then the next sequence, which would reference the above and A127585:

Error term in Stirling's approximation truncated after e^(-n).

a(n) = Floor[(sqrt(2*pi))*(n^(n+(1/2)))*(e^(-n))*(e^(1/((12*n)+1)))]

I looked at the Herbert Robbins citation, "A remark of Stirling's
Formula", Amer. Math. Monthly 62 (1955) 26-29, which is a really
lovely little elementary proof. But I don't know the next truncation
from Striling's Series, beyond the double inequality of Robbins(1958)
and Feller (1968).

Does anyone have a citation in Gosper's cute refinement as equation
(18) in the above:

n! ~ sqrt(((2*n) + (1/3))*pi) * (n^n) * (e^(-n))