A035278 - OEIS

%I #17 Dec 22 2022 04:15:42

%S 1,19,551,21489,1052961,62124699,4286604231,338641734249,

%T 30139114348161,2983772320467939,325231182931005351,

%U 38702510768789636769,4992623889173863143201,693974720595166976904939,103402233368679879558835911,16440955105620100849854909849

%N One ninth of deca-factorial numbers.

%H G. C. Greubel, <a href="/A035278/b035278.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 9*a(n) = (10*n-1)(!^10) = Product_{j=1..n} (10*j-1).

%F E.g.f.: (-1+(1-10*x)^(-9/10))/9.

%F a(n) = (Pochhammer(9/10,n) * 10^n)/9.

%F Sum_{n>=1} 1/a(n) = 9*(e/10)^(1/10)*(Gamma(9/10) - Gamma(9/10, 1/10)). - _Amiram Eldar_, Dec 22 2022

%p seq( mul(10*j-1, j=1..n)/9, n=1..20); # _G. C. Greubel_, Nov 11 2019

%t Table[10^n*Pochhammer[9/10, n]/9, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)

%o (PARI) vector(20, n, prod(j=1,n, 10*j-1)/9 ) \\ _G. C. Greubel_, Nov 11 2019

%o (Magma) [(&*[10*j-1: j in [1..n]])/9: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019

%o (Sage) [product( (10*j-1) for j in (1..n))/9 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019

%o (GAP) List([1..20], n-> Product([1..n], j-> 10*j-1)/9 ); # _G. C. Greubel_, Nov 11 2019

%Y Cf. A045757, A035265, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_