A147629 9-factorial numbers (4).

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

Offset

1,2

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

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) [Round(9^(n-1)*Gamma(n-1 +5/9)/Gamma(5/9)): n in [1..20]]; // G. C. Greubel, Dec 03 2019
(Sage) [9^(n-1)*rising_factorial(5/9, n-1) for n in (1..20)] # G. C. Greubel, Dec 03 2019

Crossrefs

Cf. A035012, A035013, A035017, A035018, A035020, A035022, A035023, A045756, A048994, A049211, A051232, A053116, A132393.

Sequence in context: A277301 A014231 A203528 * A274256 A280574 A302910

Adjacent sequences: A147626 A147627 A147628 * A147630 A147631 A147632

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Status

approved