A016309 Expansion of 1/((1-2*x)*(1-6*x)*(1-12*x)).
1, 20, 292, 3824, 47824, 585536, 7096384, 85576448, 1029436672, 12368356352, 148510974976, 1782675894272, 21395375902720, 256764101869568, 3081286768672768, 36976146501533696, 443717989683232768
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (20,-108,144)
Programs
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Magma
[(24*12^n-15*6^n+2^n)/10: n in [0..20]]; // Vincenzo Librandi, Sep 02 2011
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Mathematica
CoefficientList[Series[1/((1-2x)(1-6x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{20,-108,144},{1,20,292},30] (* Harvey P. Dale, Jul 26 2019 *)
Formula
a(n) = A071951(n+3, 3) = (24*12^n - 15*6^n + 2^n)/10. - Wolfdieter Lang, Nov 07 2003
a(n) = 18*a(n-1) - 72*a(n-2) + 2^n; a(n) = 20*a(n-1) - 108*a(n-2) + 144*a(n-3) for n > 2. - Vincenzo Librandi, Sep 02 2011
a(n) = det(|ps(i+3,j+2)|, 1 <= i,j <= n), where ps(n,k) are Legendre-Stirling numbers of the first kind (A129467). - Mircea Merca, Apr 06 2013