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A028025
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Expansion of 1/((1-3x)(1-4x)(1-5x)(1-6x)).
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2
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1, 18, 205, 1890, 15421, 116298, 830845, 5709330, 38119741, 249026778, 1599719485, 10142356770, 63639854461, 396031348458, 2448208592125, 15053605980210, 92160458747581, 562225198873338, 3419937140824765
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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. [From Wolfdieter Lang, Oct 08 2011]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (18,-119,342,-360)
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FORMULA
| If we define f(m,j,x)=sum(binomial(m,k)*stirling2(k,j)*x^(m-k),k=j..m) then a(n-3)=f(n,3,3), (n>=3). [From Milan R. Janjic (agnus(AT)blic.net), 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.: diff(exp(3*x)*((exp(x)-1)^3)/3!,x$3). [From Wolfdieter Lang, Oct 08 2011]
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CROSSREFS
| Sequence in context: A177358 A026881 A181400 * A109126 A022742 A055528
Adjacent sequences: A028022 A028023 A028024 * A028026 A028027 A028028
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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