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One seventh of deca-factorial numbers.
9

%I #16 Dec 22 2022 04:15:50

%S 1,17,459,16983,798201,45497457,3048329619,234721380663,

%T 20420760117681,1980813731415057,211947069261411099,

%U 24797807103585098583,3149321502155307520041,431457045795277130245617,63424185731905738146105699,9957597159909200888938594743

%N One seventh of deca-factorial numbers.

%H G. C. Greubel, <a href="/A035276/b035276.txt">Table of n, a(n) for n = 1..320</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

%F 7*a(n) = (10*n-3)(!^10) = Product_{j=1..n} (10*j-3).

%F E.g.f.: (-1 + (1-10*x)^(-7/10))/7.

%F a(n) = (Pochhammer(7/10,n)*10^n)/7.

%F Sum_{n>=1} 1/a(n) = 7*(e/10^3)^(1/10)*(Gamma(7/10) - Gamma(7/10, 1/10)). - _Amiram Eldar_, Dec 22 2022

%p seq( mul(10*j-3, j=1..n)/7, n=1..20); # _G. C. Greubel_, Nov 11 2019

%t Table[10^n*Pochhammer[7/10, n]/7, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)

%o (PARI) vector(20, n, prod(j=1,n, 10*j-3)/7 ) \\ _G. C. Greubel_, Nov 11 2019

%o (Magma) [(&*[10*j-3: j in [1..n]])/7: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019

%o (Sage) [product( (10*j-3) for j in (1..n))/7 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019

%o (GAP) List([1..20], n-> Product([1..n], j-> 10*j-3)/7 ); # _G. C. Greubel_, Nov 11 2019

%Y Cf. A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279, A045757.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_