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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

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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

E.g.f.: (1-9*x)^(-1/3). - Jianing Song, Dec 29 2025

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 *)

Join[{1}, FoldList[Times, NestList[#+9&, 3, 20]]] (* Harvey P. Dale, Mar 09 2025 *)

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

(SageMath) [9^n*rising_factorial(1/3, n) for n in (0..20)] # G. C. Greubel, Dec 03 2019

CROSSREFS

Row 3 of A392037.

Cf. A048994, A132393.

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

Sequence in context: A377504 A366008 A173217 * A301582 A122220 A186730

Adjacent sequences: A144755 A144756 A144757 * A144759 A144760 A144761

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Sep 20 2008

STATUS

approved

URL: https://oeis.org/A144758

⇱ A144758 - OEIS