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

0,2

Comments

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

Links

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).

Formula

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

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

Mathematica

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 *)

Prog

(Sage) [lucas_number2(n, 8, 0)*binomial(n, 7)/8^7 for n in range(7, 22)] # Zerinvary Lajos, Mar 13 2009
(Magma) [8^n* Binomial(n+7, 7): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011
(PARI) vector(30, n, n--; 8^n*binomial(n+7, 7)) \\ G. C. Greubel, Aug 16 2018

Crossrefs

Cf. A036226.

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

Sequence in context: A017211 A221424 A181241 * A330820 A000812 A240363

Adjacent sequences: A053104 A053105 A053106 * A053108 A053109 A053110

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

More terms from Harvey P. Dale, Jul 19 2018

Status

approved