A147631 a(n) = Product_{k = 1..n-1} (9*k - 2).

1, 7, 112, 2800, 95200, 4093600, 212867200, 12984899200, 908942944000, 71806492576000, 6318971346688000, 612940220628736000, 64971663386646016000, 7471741289464291840000, 926495919893572188160000, 123223957345845101025280000, 17497801943110004345589760000

Offset

1,2

Comments

Original name was: 9-factorial numbers (6).

Links

G. C. Greubel, Table of n, a(n) for n = 1..325

Formula

a(n+1) = Sum_{k=0..n} A132393(n,k)*7^k*9^(n-k). - Philippe Deléham, Nov 09 2008

a(n) = (-2)^n*Sum_{k=0..n} (9/2)^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>=1} 1/a(n) = 1 + (e/9^2)^(1/9)*(Gamma(7/9) - Gamma(7/9, 1/9)). - Amiram Eldar, Dec 21 2022

From G. C. Greubel, Dec 28 2025: (Start)

a(n) = Product_{j=0..n-2} (9*j + 7).

G.f.: (1/2)*(1 - hypergeom([1, -2/9], [], 9*x)).

E.g.f.: (1/2)*(1 - (1-9*x)^(2/9)). (End)

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 6, 2*5!, 9}]; lst
Table[9^(n-1)*Pochhammer[7/9, n-1], {n, 30}] (* G. C. Greubel, Dec 27 2025 *)

Prog

(Magma)
A147631:= func< n | n eq 1 select 1 else (&*[9*j+7: j in [0..n-2]]) >;
[A147631(n): n in [1..30]]; // G. C. Greubel, Dec 27 2025
(SageMath)
def A147631(n): return 9^(n-1)*rising_factorial(7/9, n-1)
print([A147631(n) for n in range(1, 31)]) # G. C. Greubel, Dec 27 2025

Crossrefs

Row 7 of A392037.

Cf. A048994, A132393.

Sequence in context: A067404 A129030 A128576 * A371330 A359927 A384691

Adjacent sequences: A147628 A147629 A147630 * A147632 A147633 A147634

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Extensions

New name from Jianing Song, Dec 29 2025

Status

approved