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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

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

Cf. A053108, A081139, A173000, A173187, A173188, A173191, A173192

Sequence in context: A035740 A017753 A221893 * A281580 A369144 A111599

Adjacent sequences: A197191 A197192 A197193 * A197195 A197196 A197197

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 13 2011

Status

approved