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A323588 a(n) = Product_{k=1..n} (k^n + (n-k)^n). 4
1, 1, 8, 2187, 55083008, 248292236328125, 287440081598682287308800, 136294854579772162759923622710449623, 32534104705262209051040075603284216686012438413312, 5686543339012978225006873713961872387810223003912610672810622880089 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..27

FORMULA

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.

MATHEMATICA

Table[Product[k^n+(n-k)^n, {k, 1, n}], {n, 0, 10}]

PROG

(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

CROSSREFS

Cf. A323540-A323546, A323575, A323589, A323751.

Sequence in context: A281651 A189308 A300597 * A017415 A046246 A302380

Adjacent sequences:  A323585 A323586 A323587 * A323589 A323590 A323591

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 18 2019

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)