A272248 a(n) = Product_{k=0..n} (n^5 + k^5).

0, 2, 67584, 7924375800, 2876035930521600, 2693451205324687500000, 5648896640332217707816550400, 23819277009290664033936067933468800, 185754160490281505676324140907107450880000, 2507604631016507710974687639612411760216253760000

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. A126804, A272244, A272246, A272247, A367823, A367833.

Cf. A255435, A323543, A324438.

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