|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The next terms: a(3) has 126 digits, a(4) has 743 digits, a(5) has 2927 digits.
In general, product_{k=1..n} k^(k^m) ~ A(m) * n^(B(m+1)/(m+1) + sum_{j=1..n} j^m) * exp(-n^(m+1)/(m+1)^2 + sum_{j=1..m-1} (1/(j+1) * B(j+1) * binomial(m,j) * n^(m-j) * sum_{i=0..j-1} 1/(m-i) )), where A(m) is the generalized Glaisher-Kinkelin constant (see A074962, A243262, A243263, A243264, A243265), and B(n) is the Bernoulli number A027641(n) / A027642(n).
|
|
|
REFERENCES
|
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) ~ A243265 * n^(n^2*(n+1)^2*(2*n^2+2*n-1)/12 + 1/252) / exp(47*n^2/720 - n^4/12 + n^6/36).
|
|
|
MATHEMATICA
|
Table[Product[k^(k^5), {k, 1, n}], {n, 1, 5}]
|
|
|
PROG
|
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
|
