A144827 -id:A144827 - cp's OEIS frontend

A034831 a(n) = n-th sept-factorial number divided by 4.

1, 11, 198, 4950, 158400, 6177600, 284169600, 15060988800, 903659328000, 60545174976000, 4480342948224000, 362907778806144000, 31935884534940672000, 3033909030819363840000, 309458721143575111680000, 33731000604649687173120000, 3912796070139363712081920000

Offset: 1

Wolfdieter Lang

G. C. Greubel, Table of n, a(n) for n = 1..339
Index entries for sequences related to factorial numbers.

Cf. A049209, A045754, A034829, A034830, A034832, A034833, A034834, A144827.

[(&*[(7*k-3): k in [1..n]])/4: n in [1..30]]; // G. C. Greubel, Feb 24 2018

Drop[With[{nn = 40}, CoefficientList[Series[(-1 + (1 - 7*x)^(-4/7))/4, {x, 0, nn}], x]*Range[0, nn]!], 1] (* G. C. Greubel, Feb 22 2018 *)
Table[Product[7 j - 3, {j, n}], {n, 30}]/4 (* Vincenzo Librandi, Feb 24 2018 *)

my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-4/7))/4)) \\ G. C. Greubel, Feb 22 2018

4*a(n) = (7*n-3)(!^7) = Product_{j=1..n} (7*j-3).
E.g.f.: (-1 + (1-7*x)^(-4/7))/4.
From Amiram Eldar, Dec 20 2022: (Start)
a(n) = A144827(n)/4.
Sum_{n>=1} 1/a(n) = 4*(e/7^3)^(1/7)*(Gamma(4/7) - Gamma(4/7, 1/7)). (End)

More terms added by G. C. Greubel, Feb 23 2018

A144829 Partial products of successive terms of A017209; a(0)=1 .

Original entry on oeis.org

1, 4, 52, 1144, 35464, 1418560, 69509440, 4031547520, 270113683840, 20528639971840, 1744934397606400, 164023833375001600, 16894454837625164800, 1892178941814018457600, 228953651959496233369600, 29763974754734510338048000, 4137192490908096936988672000

Offset: 0

Philippe Deléham, Sep 21 2008

			a(0)=1, a(1)=4, a(2)=4*13=52, a(3)=4*13*22=1144, a(4)=4*13*22*31=35464, ...

G. C. Greubel, Table of n, a(n) for n = 0..300

Cf. A001715, A002866, A007559, A008546, A047053.

Cf. A048994, A049308, A132393, A144827, A144828.

[n le 2 select 4^(n-1) else (9*n-14)*Self(n-1): n in [1..30]]; // G. C. Greubel, May 26 2022

Table[4*9^(n-1)*Pochhammer[13/9, n-1], {n, 0, 20}] (* Vaclav Kotesovec, Nov 29 2021 *)

a(n) = (-5)^n*sum(k=0, n, (9/5)^k*stirling(n+1,n+1-k, 1)); \\ Michel Marcus, Feb 20 2015

[9^n*rising_factorial(4/9, n) for n in (0..30)] # G. C. Greubel, May 26 2022

a(n) = Sum_{k=0..n} A132393(n,k)*4^k*9^(n-k).
a(n) = (-5)^n*Sum_{k=0..n} (9/5)^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
a(n) + (5-9*n)*a(n-1) = 0. - R. J. Mathar, Sep 04 2016
From Vaclav Kotesovec, Nov 29 2021: (Start)
a(n) = 9^n * Gamma(n + 4/9) / Gamma(4/9).
a(n) ~ sqrt(2*Pi) * 9^n * n^(n - 1/18) / (Gamma(4/9) * exp(n)). (End)
From G. C. Greubel, May 26 2022: (Start)
G.f.: hypergeometric2F0([1, 4/9], [], 9*x).
E.g.f.: (1-9*x)^(-4/9). (End)
Sum_{n>=0} 1/a(n) = 1 + (e/9^5)^(1/9)*(Gamma(4/9) - Gamma(4/9, 1/9)). - Amiram Eldar, Dec 21 2022

a(9) originally given incorrectly as 20520639971840 corrected by Peter Bala, Feb 20 2015

cp's OEIS Frontend

A034831 a(n) = n-th sept-factorial number divided by 4.

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