A144758 Partial products of successive terms of A017197.
1, 3, 36, 756, 22680, 884520, 42456960, 2420046720, 159723083520, 11979231264000, 1006255426176000, 93581754634368000, 9545338972705536000, 1059532625970314496000, 127143915116437739520000, 16401565050020468398080000, 2263415976902824638935040000
Offset: 0
Examples
a(0)=1, a(1)=3, a(2)=3*12=36, a(3)=3*12*21=756, a(4)=3*12*21*30=22680, ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..250
Crossrefs
Programs
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Magma
[Round(9^n*Gamma(n+1/3)/Gamma(1/3)): n in [0..20]]; // G. C. Greubel, Dec 03 2019
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Maple
seq(9^n*pochhammer(1/3, n), n = 0..20); # G. C. Greubel, Dec 03 2019
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Mathematica
Table[9^n*Pochhammer[1/3, n], {n, 0, 20}] (* G. C. Greubel, Dec 03 2019 *) Join[{1},FoldList[Times,NestList[#+9&,3,20]]] (* Harvey P. Dale, Mar 09 2025 *) -
PARI
a(n)=3^n*prod(i=1,n,3*i-2) \\ Charles R Greathouse IV, Jan 17 2012
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Sage
[9^n*rising_factorial(1/3, n) for n in (0..20)] # G. C. Greubel, Dec 03 2019
Formula
a(n) = Sum_{k=0..n} A132393(n,k)*3^k*9^(n-k).
a(n) = (-6)^n*Sum_{k=0..n} (3/2)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
Sum_{n>=0} 1/a(n) = 1 + (e/9^6)^(1/9)*(Gamma(1/3) - Gamma(1/3, 1/9)). - Amiram Eldar, Dec 21 2022