A197194 a(n) = binomial(n+9, 9)*9^n.
1, 90, 4455, 160380, 4691115, 118216098, 2659862205, 54717165360, 1046465787510, 18836384175180, 322102169395578, 5270762771927640, 83014513657860330, 1264374900327411180, 18694686026269579590, 269203478778281946096, 3785673920319589866975, 52108688079693178168950, 703467289075857905280825
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..400
Programs
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Magma
[Binomial(n+9, 9)*9^n: n in [0..20]];
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Mathematica
Table[Binomial[n+9,9]9^n,{n,0,20}] (* Harvey P. Dale, Feb 22 2020 *) -
Python
A197194_list, m, k = [], [1]*10, 1 for _ in range(10**2): A197194_list.append(k*m[-1]) k *= 9 for i in range(9): m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016
Formula
a(n) = C(n + 9, 9)*9^n.
G.f.: 1 / (9*x-1)^10 . - R. J. Mathar, Oct 13 2011
From Amiram Eldar, Apr 17 2022: (Start)
Sum_{n>=0} 1/a(n) = 1358954496*log(9/8) - 44817299757/280.
Sum_{n>=0} (-1)^n/a(n) = 8100000000*log(10/9) - 47791529847/56. (End)