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A147629
9-factorial numbers (4).
5
1, 5, 70, 1610, 51520, 2112320, 105616000, 6231344000, 423731392000, 32627317184000, 2805949277824000, 266565181393280000, 27722778864901120000, 3132674011733826560000, 382186229431526840320000, 50066396055530016081920000, 7009295447774202251468800000
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved