login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324443 a(n) = Product_{i=1..n, j=1..n} (1 + i^2 + j^2). 6
3, 972, 437987088, 1396064690700615936, 100943980553724942717460016640000, 408685260379151918936869901376463191556211834880000, 193581283410907012468703321819613695893448022144552623141894180044800000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Product_{i>=1, j>=1} (1 + 1/(i^2 + j^2)) = is divergent.

LINKS

Table of n, a(n) for n=1..7.

FORMULA

a(n) ~ c * 2^(n*(n+1)) * exp(Pi*n*(n+1)/2 - 3*n^2) * n^(2*n^2 + (Pi - 1)/2), where c = A306398 = 0.1740394919107672354475619059102344818913844938434521480869...

a(n) / A324403(n) ~ d * n^(Pi/2), where d = A306398 * 2^(3/4) * exp(-Pi/12) * Pi^(1/4) * Gamma(3/4) = 0.36753062884677326134620846786416595535234038999313...

MATHEMATICA

Table[Product[1 + i^2 + j^2, {i, 1, n}, {j, 1, n}], {n, 1, 10}]

CROSSREFS

Cf. A101686, A324403, A324425, A324444, A306398.

Sequence in context: A332193 A167058 A167067 * A151585 A286525 A030250

Adjacent sequences:  A324440 A324441 A324442 * A324444 A324445 A324446

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Feb 28 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 17:46 EST 2022. Contains 350484 sequences. (Running on oeis4.)