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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (20,-108,144)

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

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 *)

Prog

(Magma) [(24*12^n-15*6^n+2^n)/10: n in [0..20]]; // Vincenzo Librandi, Sep 02 2011

Crossrefs

Cf. A089278, A089500.

Sequence in context: A384326 A395705 A016261 * A190824 A016259 A271029

Adjacent sequences: A016306 A016307 A016308 * A016310 A016311 A016312

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved