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URL: https://oeis.org/A034829

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A034829
a(n) = n-th sept-factorial number divided by 2.
9
1, 9, 144, 3312, 99360, 3676320, 161758080, 8249662080, 478480400640, 31101226041600, 2239288274995200, 176903773724620800, 15213724540317388800, 1414876382249517158400, 141487638224951715840000, 15139177290069833594880000, 1725866211067961029816320000
OFFSET
1,2
FORMULA
2*a(n) = (7*n-5)(!^7) = Product_{j=1..n} (7*j-5).
E.g.f.: (-1 + (1-7*x)^(-2/7))/2.
D-finite with recurrence: a(n) +(-7*n+5)*a(n-1)=0. - R. J. Mathar, Feb 24 2020
From Amiram Eldar, Dec 19 2022: (Start)
a(n) = A084947(n)/2.
Sum_{n>=1} 1/a(n) = 2*(e/7^5)^(1/7)*(Gamma(2/7) - Gamma(2/7, 1/7)). (End)
MATHEMATICA
Drop[With[{nn = 50}, CoefficientList[Series[(-1 + (1 - 7*x)^(-2/7))/2, {x, 0, nn}], x]*Range[0, nn]!], 1] (* G. C. Greubel, Feb 23 2018 *)
PROG
(PARI) vector(20, n, prod(j=1, n, 7*j-5)/2) \\ Michel Marcus, Jan 07 2015
KEYWORD
easy,nonn
STATUS
approved