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

%I

%S 1,1,65,47449,194444416,3038449102976,141766192358448256,

%T 16678817447073033946240,4372271021740050216976646144,

%U 2323608852183697867526563204694016,2323611343146528421975097303187359268864,4116421685969107286571222251382158945547976704

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

%H Vaclav Kotesovec, <a href="/A269794/b269794.txt">Table of n, a(n) for n = 0..100</a>

%F 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

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

%o (PARI) {a(n)=n!^6*polcoeff(prod(k=1, n, 1/(1-x^k/k^6 +x*O(x^n))), n)}

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

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

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 05 2016

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Last modified July 12 06:48 EDT 2020. Contains 335657 sequences. (Running on oeis4.)