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A028025 Expansion of 1/((1-3x)(1-4x)(1-5x)(1-6x)). 3
1, 18, 205, 1890, 15421, 116298, 830845, 5709330, 38119741, 249026778, 1599719485, 10142356770, 63639854461, 396031348458, 2448208592125, 15053605980210, 92160458747581, 562225198873338, 3419937140824765 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
This gives the fourth column of the Sheffer triangle A143495 (3-restricted Stirling2 numbers). See the e.g.f. given below, and comments on the general case under A193685. - Wolfdieter Lang, Oct 08 2011
LINKS
FORMULA
If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-3) = f(n,3,3), (n >= 3). - Milan Janjic, Apr 26 2009
a(n) = -5^(n+3)/2 + 2*4^(n+2)+ 6^(n+2) - 3^(n+2)/2. - R. J. Mathar, Mar 22 2011
O.g.f.: 1/((1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)).
E.g.f.: (d^3/dx^3)(exp(3*x)*((exp(x)-1)^3)/3!). - Wolfdieter Lang, Oct 08 2011]
MATHEMATICA
CoefficientList[Series[1/((1-3x)(1-4x)(1-5x)(1-6x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{18, -119, 342, -360}, {1, 18, 205, 1890}, 30] (* Harvey P. Dale, Jan 29 2024 *)
PROG
(PARI) Vec(1/((1-3*x)*(1-4*x)*(1-5*x)*(1-6*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
Sequence in context: A181400 A282020 A277763 * A109126 A022742 A055528
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified May 21 19:35 EDT 2024. Contains 372738 sequences. (Running on oeis4.)