|
| |
|
|
A143476
|
|
Denominator of the coefficient of z^(2n) in the Stirling-like asymptotic expansion of the hyperfactorial function A002109.
|
|
1
|
|
|
|
1, 720, 7257600, 15676416000, 3476402012160000, 162695614169088000000, 4919915372473221120000000, 60219764159072226508800000000, 507464726196802564122476544000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
In Glaisher (1878) equation (2) is 1^1.2^2.3^3 ... n^n = A n^(n^2/2 + n/2 + 1/12) e^(-n^4/4) (1 + 1/(720n^2) - 1433/(7257600n^4) + &c.) - Michael Somos, Jun 24 2012
|
|
|
REFERENCES
|
J. W. L. Glaisher, On The Product 1^1.2^2.3^3 ... n^n, Messenger of Mathematics, 7 (1878), pp. 43-47, see p. 43 eq. (2)
|
|
|
LINKS
|
Table of n, a(n) for n=0..8.
Eric Weisstein's World of Mathematics, Hyperfactorial
|
|
|
EXAMPLE
|
(Glaisher*(1 - 1433/(7257600*z^4) + 1/(720*z^2))*z^(1/12 + (z*(1 + z))/2))/E^(z^2/4)
|
|
|
CROSSREFS
|
Cf. A002109, A143475.
Sequence in context: A030185 A010799 A075754 * A008979 A158044 A181751
Adjacent sequences: A143473 A143474 A143475 * A143477 A143478 A143479
|
|
|
KEYWORD
|
nonn,frac
|
|
|
AUTHOR
|
Eric W. Weisstein, Aug 19, 2008
|
|
|
STATUS
|
approved
|
| |
|
|
