A173188 -id:A173188 - cp's OEIS frontend

A173191 a(n) = binomial(n + 6, 6)*9^n.

1, 63, 2268, 61236, 1377810, 27280638, 491051484, 8207574804, 129269303163, 1939039547445, 27922169483208, 388371993720984, 5243021915233284, 68965903654222428, 886704475554288360, 11172476391984033336, 138259395350802412533, 1683511461036241140843

Offset: 0

Zerinvary Lajos, Feb 12 2010

Number of n-permutations (n>=6) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly six (6) u's.

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (63,-1701,25515,-229635,1240029,-3720087,4782969).

Cf. A081139, A173000, A173187, A173188.

[Binomial(n+6, 6)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011

A173191:=n->binomial(n+6,6)*9^n: seq(A173191(n), n=0..25); # Wesley Ivan Hurt, Jul 24 2017

Table[Binomial[n + 6, 6]*9^n, {n, 0, 20}]

a(n) = C(n + 6, 6)*9^n.
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 1042074/5 - 1769472*log(9/8).
Sum_{n>=0} (-1)^n/a(n) = 5400000*log(10/9) - 2844729/5. (End)

A173192 a(n) = binomial(n + 7, 7)*9^n.

Original entry on oeis.org

1, 72, 2916, 87480, 2165130, 46766808, 911952756, 16415149608, 277005649635, 4432090394160, 67810983030648, 998670840996816, 14231059484204628, 197045439012064080, 2660113426662865080, 35113497231949819056, 454280870438350784037, 5772039294981398197176

Offset: 0

Zerinvary Lajos, Feb 12 2010

Number of n-permutations (n>=7) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 7 u's.

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (72,-2268,40824,-459270,3306744,-14880348,38263752,-43046721).

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

[Binomial(n+7, 7)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011

A173192:=n->binomial(n+7,7)*9^n: seq(A173192(n), n=0..25); # Wesley Ivan Hurt, Jul 24 2017

Table[Binomial[n + 7, 7]*9^n, {n, 0, 20}]

a(n) = C(n + 7, 7)*9^n.
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 16515072*log(9/8) - 19451943/10.
Sum_{n>=0} (-1)^n/a(n) = 63000000*log(10/9) - 13275423/2. (End)

A196221 Binomial(n+10, 10)*9^n.

Original entry on oeis.org

1, 99, 5346, 208494, 6567561, 177324147, 4255779528, 93019181112, 1883638417518, 35789129932842, 644204338791156, 11068601821048044, 182631930047292726, 2908062270753045714, 44867246463046991016, 673008696945704865240, 9842752192830933654135, 140693457815171581056165, 1969708409412402134786310

Offset: 0

Vincenzo Librandi, Oct 13 2011

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

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

Magma
```
[Binomial(n+10, 10)*9^n: n in [0..20]];
```

a(n) = C(n+10, 10)*9^n.

G.f. -1 / (9*x-1)^11 . - R. J. Mathar, Oct 13 2011

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

Original entry on oeis.org

1, 90, 4455, 160380, 4691115, 118216098, 2659862205, 54717165360, 1046465787510, 18836384175180, 322102169395578, 5270762771927640, 83014513657860330, 1264374900327411180, 18694686026269579590, 269203478778281946096, 3785673920319589866975, 52108688079693178168950, 703467289075857905280825

Offset: 0

Vincenzo Librandi, Oct 13 2011

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

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

Magma
```
[Binomial(n+9, 9)*9^n: n in [0..20]];
```

Table[Binomial[n+9,9]9^n,{n,0,20}] (* Harvey P. Dale, Feb 22 2020 *)

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

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)

cp's OEIS Frontend

A173191 a(n) = binomial(n + 6, 6)*9^n.

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A173192 a(n) = binomial(n + 7, 7)*9^n.

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A196221 Binomial(n+10, 10)*9^n.

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Magma

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

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Magma

Mathematica

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