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
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).
Programs
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Magma
[6^n* Binomial(n+5, 5): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
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Maple
seq(binomial(n+5,5)*6^n,n=0..17); # Zerinvary Lajos, Jun 16 2008
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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 *) -
Sage
[lucas_number2(n, 6, 0)*binomial(n,5)/6^5 for n in range(5, 23)] # Zerinvary Lajos, Mar 13 2009
Formula
a(n) = 6^n*binomial(n+5, 5).
G.f.: 1/(1-6*x)^6.
a(n) = 36*a(n-1) - 540*a(n-2) + 4320*a(n-3) - 19440*a(n-4) + 46656*a(n-5) - 46656*a(n-6). - Wesley Ivan Hurt, Jul 07 2025