A269793 G.f.: Product_{n>=1} 1/(1 - x^n/n^5) = Sum_{n>=0} a(n)*x^n/n!^5.

1, 1, 33, 8051, 8259776, 25822962624, 200839327164224, 3375758721819353792, 110621043661751405543424, 6532189550762931700406452224, 653226327065916563182761815212032, 105203470361723800472334968046839365632, 26178104032796403698593899646317901702496256

Offset

0,3

Links

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

Formula

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

Mathematica

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

Prog

(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), ", "))

Crossrefs

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

Sequence in context: A183237 A099828 A099827 * A336197 A336261 A060705

Adjacent sequences: A269790 A269791 A269792 * A269794 A269795 A269796

Keyword

nonn

Author

Vaclav Kotesovec, Mar 05 2016

Status

approved