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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

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

Example

a(0)=1, a(1)=3, a(2)=3*12=36, a(3)=3*12*21=756, a(4)=3*12*21*30=22680, ...

Maple

seq(9^n*pochhammer(1/3, n), n = 0..20); # G. C. Greubel, Dec 03 2019

Mathematica

Table[9^n*Pochhammer[1/3, n], {n, 0, 20}] (* G. C. Greubel, Dec 03 2019 *)

Prog

(PARI) a(n)=3^n*prod(i=1, n, 3*i-2) \\ Charles R Greathouse IV, Jan 17 2012
(Magma) [Round(9^n*Gamma(n+1/3)/Gamma(1/3)): n in [0..20]]; // G. C. Greubel, Dec 03 2019
(Sage) [9^n*rising_factorial(1/3, n) for n in (0..20)] # G. C. Greubel, Dec 03 2019

Crossrefs

Cf. A048994, A132393.

Cf. A001710, A001147, A008545, A011781, A032031, A047056, A144739, A144756.

Sequence in context: A193754 A366008 A173217 * A301582 A122220 A186730

Adjacent sequences: A144755 A144756 A144757 * A144759 A144760 A144761

Keyword

nonn,easy

Author

Philippe Deléham, Sep 20 2008

Status

approved