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A272248 a(n) = Product_{k=0..n} (n^5 + k^5). 4
0, 2, 67584, 7924375800, 2876035930521600, 2693451205324687500000, 5648896640332217707816550400, 23819277009290664033936067933468800, 185754160490281505676324140907107450880000, 2507604631016507710974687639612411760216253760000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, for p>=1, Product_{k=0..n} (n^p + k^p) ~ sqrt(2) * n^(p*(n+1)) * exp(n*Sum_{j>=1} (-1)^(j+1) / (j*(1 + j*p))).

LINKS

Table of n, a(n) for n=0..9.

FORMULA

a(n) ~ 2^(2*n+1/2) * phi^(sqrt(5)*n) * n^(5*n+5) / exp((5-sqrt(phi)*Pi/5^(1/4))*n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.

MATHEMATICA

Table[Product[n^5+k^5, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Cf. A255435, A272244, A272246, A272247, A323543.

Sequence in context: A060895 A100266 A272137 * A195003 A071067 A321246

Adjacent sequences:  A272245 A272246 A272247 * A272249 A272250 A272251

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Apr 23 2016

STATUS

approved

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Last modified March 26 12:43 EDT 2019. Contains 321497 sequences. (Running on oeis4.)