

A324443


a(n) = Product_{i=1..n, j=1..n} (1 + i^2 + j^2).


6



3, 972, 437987088, 1396064690700615936, 100943980553724942717460016640000, 408685260379151918936869901376463191556211834880000, 193581283410907012468703321819613695893448022144552623141894180044800000000
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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: A210768 A167058 A167067 * A151585 A286525 A030250
Adjacent sequences: A324440 A324441 A324442 * A324444 A324445 A324446


KEYWORD

nonn


AUTHOR

Vaclav Kotesovec, Feb 28 2019


STATUS

approved



