A354054 a(n) = Product_{k=0..n} (k^6 + 1).

1, 2, 130, 94900, 388805300, 6075471617800, 283463279271694600, 33349454806314869690000, 8742392830201411514885050000, 4646074730467898538293540742100000, 4646079376542629006192079035640742100000, 8230817672466612927467651920537784356160200000

Offset: 0

Author

Vaclav Kotesovec, May 16 2022

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..103

Crossrefs

Cf. A002604, A101686, A255433, A255434, A258871, A354052.

Programs

Maple

A354054 := proc(n)
    mul( k^6+1,k=0..n) ;
end proc:
seq(A354054(n),n=0..40) ; # R. J. Mathar, Jul 17 2023

Mathematica

Table[Product[k^6 + 1, {k, 0, n}], {n, 0, 15}]

PARI

a(n) = prod(k=1, n, k^6+1);

Formula

a(n) ~ (2*sinh(2*Pi) - 4*sinh(Pi)*cos(sqrt(3)*Pi)) * n^(6*n + 3) / exp(6*n).

a(n) ~ A258871 * (n!)^6.