cp's OEIS Frontend

A197194 a(n) = binomial(n+9, 9)*9^n.

%I A197194 #23 Apr 17 2022 08:23:12
%S A197194 1,90,4455,160380,4691115,118216098,2659862205,54717165360,
%T A197194 1046465787510,18836384175180,322102169395578,5270762771927640,
%U A197194 83014513657860330,1264374900327411180,18694686026269579590,269203478778281946096,3785673920319589866975,52108688079693178168950,703467289075857905280825
%N A197194 a(n) = binomial(n+9, 9)*9^n.
%H A197194 Vincenzo Librandi, <a href="/A197194/b197194.txt">Table of n, a(n) for n = 0..400</a>
%F A197194 a(n) = C(n + 9, 9)*9^n.
%F A197194 G.f.: 1 / (9*x-1)^10 . - _R. J. Mathar_, Oct 13 2011
%F A197194 From _Amiram Eldar_, Apr 17 2022: (Start)
%F A197194 Sum_{n>=0} 1/a(n) = 1358954496*log(9/8) - 44817299757/280.
%F A197194 Sum_{n>=0} (-1)^n/a(n) = 8100000000*log(10/9) - 47791529847/56. (End)
%t A197194 Table[Binomial[n+9,9]9^n,{n,0,20}] (* _Harvey P. Dale_, Feb 22 2020 *)
%o A197194 (Magma) [Binomial(n+9, 9)*9^n: n in [0..20]];
%o A197194 (Python)
%o A197194 A197194_list, m, k = [], [1]*10, 1
%o A197194 for _ in range(10**2):
%o A197194     A197194_list.append(k*m[-1])
%o A197194     k *= 9
%o A197194     for i in range(9):
%o A197194         m[i+1] += m[i] # _Chai Wah Wu_, Jan 24 2016
%Y A197194 Cf. A053108, A081139, A173000, A173187, A173188, A173191, A173192
%K A197194 nonn,easy
%O A197194 0,2
%A A197194 _Vincenzo Librandi_, Oct 13 2011