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A028085 Expansion of 1/((1-3x)(1-6x)(1-9x)(1-12x)). 3
1, 30, 585, 9450, 137781, 1888110, 24862545, 318755250, 4012058061, 49847787990, 613622150505, 7503229474650, 91300979746341, 1106997911204670, 13386607046238465, 161563913916523650 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

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

Fourth column of triangle A075498.

Cf. A017933, A075515.

Sequence in context: A028092 A028126 A028016 * A028012 A028011 A028072

Adjacent sequences:  A028082 A028083 A028084 * A028086 A028087 A028088

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 20 18:38 EST 2022. Contains 350472 sequences. (Running on oeis4.)