A034787 a(n) = n-th sextic factorial number divided by 5.
1, 11, 187, 4301, 124729, 4365515, 178986115, 8412347405, 445854412465, 26305410335435, 1709851671803275, 121399468698032525, 9347759089748504425, 775864004449125867275, 69051896395972202187475, 6559930157617359207810125, 662552945919353279988822625
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..345
Programs
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GAP
List([1..20], n-> Product([1..n], j-> 6*j-1)/5 ); # G. C. Greubel, Nov 11 2019
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Magma
[(&*[6*j-1: j in [1..n]])/5: n in [1..20]]; // G. C. Greubel, Nov 11 2019
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Maple
seq( mul(6*j-1, j=1..n)/5, n=1..20); # G. C. Greubel, Nov 11 2019
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Mathematica
Table[6^n*Pochhammer[5/6, n]/5, {n,20}] (* G. C. Greubel, Nov 11 2019 *) With[{nn=20},CoefficientList[Series[(-1+(1-6x)^(-5/6))/5,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Dec 21 2024 *) -
PARI
vector(20, n, prod(j=1,n, 6*j-1)/5 ) \\ G. C. Greubel, Nov 11 2019
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Sage
[product( (6*j-1) for j in (1..n))/5 for n in (1..20)] # G. C. Greubel, Nov 11 2019
Formula
5*a(n) = (6*n-1)(!^6) = Product_{j=1..n} (6*j-1) = (6*n)!/(3^(2*n)*2^(2*n+1)*(2*n)!*A008542(n)*A007559(n)*A034000(n)).
E.g.f.: (-1 + (1-6*x)^(-5/6))/5.
a(n+1) ~ sqrt(2*Pi) * 6/(5*Gamma(5/6)) * n^(4/3) * (6*n/e)^n * (1 + (61/72)/n + ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
D-finite with recurrence: a(n) +(-6*n+1)*a(n-1)=0. - R. J. Mathar, Feb 24 2020
Sum_{n>=1} 1/a(n) = 5*(e/6)^(1/6)*(Gamma(5/6) - Gamma(5/6, 1/6)). - Amiram Eldar, Dec 18 2022