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%I #18 Dec 22 2022 04:15:53
%S 1,13,299,9867,424281,22486893,1416674259,103417220907,8583629335281,
%T 798277528181133,82222585402656699,9291152150500206987,
%U 1142811714511525459401,151993958030032886100333,21735135998294702712347619,3325475807739089514989185707,542052556661471590943237270241
%N One third of deca-factorial numbers.
%H G. C. Greubel, <a href="/A035272/b035272.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 3*a(n) = (10*n-7)(!^10) = Product_{j=1..n} (10*j-7).
%F E.g.f.: (-1 + (1-10*x)^(-3/10))/3.
%F Sum_{n>=1} 1/a(n) = 3*(e/10^7)^(1/10)*(Gamma(3/10) - Gamma(3/10, 1/10)). - _Amiram Eldar_, Dec 22 2022
%p seq( mul(10*j-7, j=1..n)/3, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t Table[10^n*Pochhammer[3/10, n]/3, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o (PARI) vector(20, n, prod(j=1,n, 10*j-7)/3 ) \\ _G. C. Greubel_, Nov 11 2019
%o (Magma) [(&*[10*j-7: j in [1..n]])/3: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o (Sage) [product( (10*j-7) for j in (1..n))/3 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o (GAP) List([1..20], n-> Product([1..n], j-> 10*j-7)/3 ); # _G. C. Greubel_, Nov 11 2019
%Y Cf. A035273, A035274, A035275, A035276, A035277, A035278, A035279, A045757.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
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