0,3

Vaclav Kotesovec, Table of n, a(n) for n = 0..120

a(n) ~ c * n!^5, where c = Product_{k>=2} 1/(1-1/k^5) = abs(Gamma((9+sqrt(5) + i*sqrt(10-2*sqrt(5)))/4) * Gamma((9-sqrt(5) + i*sqrt(10+2*sqrt(5)))/4))^2 = 1.03814501733099931382497266723652151296563..., where Gamma is the Gamma function and i is the imaginary unit. - Vaclav Kotesovec, Mar 05 2016

Table[n!^5 * SeriesCoefficient[Product[1/(1-x^k/k^5), {k, 1, n}], {x, 0, n}], {n, 0, 20}]

(PARI) {a(n)=n!^5*polcoeff(prod(k=1, n, 1/(1-x^k/k^5 +x*O(x^n))), n)}

for(n=0, 20, print1(a(n), ", "))

Cf. A007841, A249588, A249593, A269791, A269794.

Sequence in context: A183237 A099828 A099827 * A373876 A336197 A336261

Adjacent sequences: A269790 A269791 A269792 * A269794 A269795 A269796

Vaclav Kotesovec, Mar 05 2016

approved