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A323588
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a(n) = Product_{k=1..n} (k^n + (n-k)^n).
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4
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1, 1, 8, 2187, 55083008, 248292236328125, 287440081598682287308800, 136294854579772162759923622710449623, 32534104705262209051040075603284216686012438413312, 5686543339012978225006873713961872387810223003912610672810622880089
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..27
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FORMULA
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a(n) ~ c * 2^(n^2) * n^(n^2) / exp(n^2), where
c = 1.7567468186007109703792640049745420817202851050652253469714... if n is even,
c = 1.8080216158688347442204158454365469233524049331246880759722... if n is odd.
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MATHEMATICA
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Table[Product[k^n+(n-k)^n, {k, 1, n}], {n, 0, 10}]
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PROG
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(PARI) vector(10, n, n--; prod(k=1, n, k^n+(n-k)^n)) \\ G. C. Greubel, Feb 08 2019
(Magma) [1] cat [(&*[k^n +(n-k)^n: k in [1..n]]): n in [1..10]]; // G. C. Greubel, Feb 08 2019
(Sage) [product(k^n +(n-k)^n for k in (1..n)) for n in (0..10)] # G. C. Greubel, Feb 08 2019
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CROSSREFS
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Cf. A323540-A323546, A323575, A323589, A323751.
Sequence in context: A281651 A189308 A300597 * A017415 A046246 A302380
Adjacent sequences: A323585 A323586 A323587 * A323589 A323590 A323591
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Jan 18 2019
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STATUS
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approved
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