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URL: https://oeis.org/A016109

⇱ A016109 - OEIS

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A016109
Expansion of 1/((1-7*x)*(1-8*x)*(1-9*x)*(1-10*x)).
6
1, 34, 725, 12410, 186501, 2571114, 33339685, 413066170, 4941549701, 57504755594, 654463491045, 7314256515930, 80522026412101, 875355238834474, 9415203971344805, 100355146006589690, 1061398586003869701, 11150995978392023754, 116475767141990660965, 1210523066880849655450
OFFSET
0,2
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,3,7), n >= 3. - Milan Janjic, Apr 26 2009; adapted by R. J. Mathar, Mar 15 2011
a(n) = 19*a(n-1) - 90*a(n-2) + 8^(n+1) - 7^(n+1), n >= 2. - Vincenzo Librandi, Mar 12 2011
a(n) = (10^(n+3) - 3*9^(n+3) + 3*8^(n+3) - 7^(n+3))/6. - Bruno Berselli, Mar 12 2011
a(n) = 34*a(n-1) - 431*a(n-2) + 2414*a(n-3) - 5040*a(n-4); a(0)=1, a(1)=34, a(2)=725, a(3)=12410. - Harvey P. Dale, Jan 26 2012
MATHEMATICA
CoefficientList[Series[1/((1-7x)(1-8x)(1-9x)(1-10x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{34, -431, 2414, -5040}, {1, 34, 725, 12410}, 21] (* Harvey P. Dale, Jan 26 2012 *)
KEYWORD
nonn,easy
EXTENSIONS
Offset changed to 0 by Vincenzo Librandi, Mar 12 2011
a(16) onward from Andrew Howroyd, Nov 07 2025
STATUS
approved