A269794 G.f.: Product_{n>=1} 1/(1 - x^n/n^6) = Sum_{n>=0} a(n)*x^n/n!^6.

1, 1, 65, 47449, 194444416, 3038449102976, 141766192358448256, 16678817447073033946240, 4372271021740050216976646144, 2323608852183697867526563204694016, 2323611343146528421975097303187359268864, 4116421685969107286571222251382158945547976704

Offset: 0

Author

Vaclav Kotesovec, Mar 05 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A007841, A249588, A249593, A269791, A269793.

Programs

Mathematica

Table[n!^6 * SeriesCoefficient[Product[1/(1-x^k/k^6), {k, 1, n}], {x, 0, n}], {n, 0, 20}]

PARI

{a(n)=n!^6*polcoeff(prod(k=1, n, 1/(1-x^k/k^6 +x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))

Formula

a(n) ~ c * n!^6, where c = Product_{k>=2} 1/(1-1/k^6) = 6*Pi^2 / cosh(sqrt(3)*Pi/2)^2 = 1.0176208398261870492814795459985... . - Vaclav Kotesovec, Mar 05 2016