A147629 a(n) = Product_{k = 1..n-1} (9*k - 4).

1, 5, 70, 1610, 51520, 2112320, 105616000, 6231344000, 423731392000, 32627317184000, 2805949277824000, 266565181393280000, 27722778864901120000, 3132674011733826560000, 382186229431526840320000, 50066396055530016081920000, 7009295447774202251468800000

Offset

1,2

Comments

Original name was: 9-factorial numbers (4).

Links

G. C. Greubel, Table of n, a(n) for n = 1..300

Formula

a(n+1) = Sum_{k=0..n} A132393(n,k)*5^k*9^(n-k). - Philippe Deléham, Nov 09 2008

From R. J. Mathar, Nov 09 2008: (Start)

a(n) = a(n-1) + (4 + 9*(n-2))*a(n-1) = (9*n-13)*a(n-1).

a(n) = 9^(n-1)*Gamma(n-4/9)/Gamma(5/9).

G.f.: z*2F0(5/9,1; -; 9*z). (End)

a(n) = (-4)^n*Sum_{k=0..n} (9/4)^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>=1} 1/a(n) = 1 + (e/9^4)^(1/9)*(Gamma(5/9) - Gamma(5/9, 1/9)). - Amiram Eldar, Dec 21 2022

E.g.f.: with offset 0: (1-9*x)^(-5/9). - Jianing Song, Dec 29 2025

E.g.f.: (1/4)*(1 - (1-9*x)^(4/9)). - G. C. Greubel, Dec 29 2025

Maple

seq(9^(n-1)*pochhammer(5/9, n-1), n = 1..20); # G. C. Greubel, Dec 03 2019

Mathematica

Table[9^(n-1)*Pochhammer[5/9, n-1], {n, 20}] (* G. C. Greubel, Dec 03 2019 *)

Prog

(PARI) vector(20, n, prod(j=0, n-2, 9*j+5) ) \\ G. C. Greubel, Dec 03 2019
(Magma)
A147629:= func< n | n le 1 select n else (&*[9*j-4: j in [1..n-1]]) >;
[A147629(n): n in [1..30]]; // G. C. Greubel, Dec 03 2019; Dec 29 2025
(SageMath) [9^(n-1)*rising_factorial(5/9, n-1) for n in (1..20)] # G. C. Greubel, Dec 03 2019

Crossrefs

Row 5 of A392037.

Cf. A048994, A132393.

Sequence in context: A014231 A203528 A396795 * A274256 A280574 A302910

Adjacent sequences: A147626 A147627 A147628 * A147630 A147631 A147632

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Extensions

New name from Jianing Song, Dec 29 2025

Status

approved