This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 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 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

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.

Last modified December 15 04:23 EST 2019. Contains 329991 sequences. (Running on oeis4.)