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A197194 a(n) = binomial(n+9, 9)*9^n. 1
1, 90, 4455, 160380, 4691115, 118216098, 2659862205, 54717165360, 1046465787510, 18836384175180, 322102169395578, 5270762771927640, 83014513657860330, 1264374900327411180, 18694686026269579590, 269203478778281946096, 3785673920319589866975, 52108688079693178168950, 703467289075857905280825 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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)
MATHEMATICA
Table[Binomial[n+9, 9]9^n, {n, 0, 20}] (* Harvey P. Dale, Feb 22 2020 *)
PROG
(Magma) [Binomial(n+9, 9)*9^n: n in [0..20]];
(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
CROSSREFS
Sequence in context: A035740 A017753 A221893 * A281580 A369144 A111599
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 13 2011
STATUS
approved

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Last modified June 22 22:28 EDT 2024. Contains 373622 sequences. (Running on oeis4.)