A036084 Expansion of 1/(1-6*x)^6.

1, 36, 756, 12096, 163296, 1959552, 21555072, 221709312, 2161665792, 20175547392, 181579926528, 1584697540608, 13469929095168, 111904026329088, 911218500108288, 7289748000866304, 57406765506822144, 445746649817677824

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (36, -540, 4320, -19440, 46656, -46656).

Formula

a(n) = 6^n*binomial(n+5, 5).

G.f.: 1/(1-6*x)^6.

Maple

seq(binomial(n+5, 5)*6^n, n=0..17); # Zerinvary Lajos, Jun 16 2008

Mathematica

CoefficientList[Series[1/(1-6x)^6, {x, 0, 30}], x] (* or *) LinearRecurrence[ {36, -540, 4320, -19440, 46656, -46656}, {1, 36, 756, 12096, 163296, 1959552}, 30] (* Harvey P. Dale, Jul 31 2018 *)

Prog

(Sage)[lucas_number2(n, 6, 0)*binomial(n, 5)/6^5for n in range(5, 23)] # Zerinvary Lajos, Mar 13 2009]
(Magma) [6^n* Binomial(n+5, 5): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011

Crossrefs

Cf. A001787, A036071.

Sequence in context: A215768 A320821 A144941 * A265194 A280123 A004338

Adjacent sequences: A036081 A036082 A036083 * A036085 A036086 A036087

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved