A175210 -id:A175210 - cp's OEIS frontend

A053107 Expansion of 1/(1-8*x)^8.

1, 64, 2304, 61440, 1351680, 25952256, 449839104, 7197425664, 107961384960, 1535450808320, 20882130993152, 273366078455808, 3462636993773568, 42617070692597760, 511404848311173120, 6000483553517764608, 69005560865454292992, 779356922715719073792

Offset: 0

Wolfdieter Lang

With a different offset, number of n-permutations (n>=7) of 9 objects: p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly 7 u's. - Zerinvary Lajos, Feb 11 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (64, -1792, 28672, -286720, 1835008, -7340032, 16777216, -16777216).

Cf. A036226.

Cf. A081138, A140802, A175210, A140406, A053107, A141054, A173155. - Zerinvary Lajos, Feb 11 2010

[8^n* Binomial(n+7, 7): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

Table[Binomial[n + 7, 7]*8^n, {n, 0, 20}] (* Zerinvary Lajos, Feb 11 2010 *)
CoefficientList[Series[1/(1-8x)^8,{x,0,20}],x] (* or *) LinearRecurrence[ {64,-1792,28672,-286720,1835008,-7340032,16777216,-16777216},{1,64,2304,61440,1351680,25952256,449839104,7197425664},20] (* Harvey P. Dale, Jul 19 2018 *)

vector(30, n, n--; 8^n*binomial(n+7,7)) \\ G. C. Greubel, Aug 16 2018

[lucas_number2(n, 8, 0)*binomial(n,7)/8^7 for n in range(7, 22)] # Zerinvary Lajos, Mar 13 2009

a(n) = 8^n*binomial(n+7, 7).

G.f.: 1/(1-8*x)^8.

More terms from Harvey P. Dale, Jul 19 2018

A173155 a(n) = binomial(n + 5, 5) * 8^n.

Original entry on oeis.org

1, 48, 1344, 28672, 516096, 8257536, 121110528, 1660944384, 21592276992, 268703891456, 3224446697472, 37520834297856, 425236122042368, 4710307813392384, 51140484831117312, 545498504865251328, 5727734301085138944, 59298896293587320832, 606166495445559279616

Offset: 0

Zerinvary Lajos, Feb 11 2010

With a different offset, number of n-permutations (n>=5) of 9 objects: p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly five (5) u's.

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (48,-960,10240,-61440,196608,-262144).

Cf. A081138, A140802, A175210, A140406, A053107, A141054.

[8^n* Binomial(n+5, 5): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

Table[Binomial[n + 5, 5]*8^n, {n, 0, 20}]

a(n) = C(n + 5, 5)*8^n, n>=0.
G.f.: 1/(1-8*x)^6. - Vincenzo Librandi, Oct 16 2011
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 96040*log(8/7) - 38470/3.
Sum_{n>=0} (-1)^n/a(n) = 262440*log(9/8) - 30910. (End)

cp's OEIS Frontend

A053107 Expansion of 1/(1-8*x)^8.

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