OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (30,-315,1350,-1944).
FORMULA
a(n) = (3^n)*Stirling2(n+4, 4), n >= 0, with Stirling2(n, m) = A008277(n, m).
a(n) = Sum_{m=0..3} (A075513(4, m)*((m+1)*3)^n)/3!.
G.f.: 1/Product_{k=1..4} (1-3*k*x).
E.g.f.: (d^4/dx^4)((((exp(3*x)-1)/3)^4)/4!) = Sum_{m=0..3} (A075513(4, m)*exp(3*(m+1)*x))/3!.
a(n) = (12^(n+3) - 3*9^(n+3) + 3*6^(n+3) - 3^(n+3))/162. - Yahia Kahloune, Jun 10 2013
a(0)=1, a(1)=30, a(2)=585, a(3)=9450, a(n) = 30*a(n-1) - 315*a(n-2) + 1350*a(n-3) - 1944*a(n-4). - Harvey P. Dale, Feb 06 2015
MATHEMATICA
CoefficientList[Series[1/((1-3x)(1-6x)(1-9x)(1-12x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{30, -315, 1350, -1944}, {1, 30, 585, 9450}, 30] (* Harvey P. Dale, Feb 06 2015 *)
PROG
(PARI) Vec(1/((1-3*x)*(1-6*x)*(1-9*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved