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A101859
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a(n) = 11 + (23*n)/2 + n^2/2.
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9
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0, 11, 23, 36, 50, 65, 81, 98, 116, 135, 155, 176, 198, 221, 245, 270, 296, 323, 351, 380, 410, 441, 473, 506, 540, 575, 611, 648, 686, 725, 765, 806, 848, 891, 935, 980, 1026, 1073, 1121, 1170, 1220, 1271, 1323, 1376, 1430, 1485, 1541, 1598, 1656, 1715, 1775, 1836
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OFFSET
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-1,2
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LINKS
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FORMULA
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If we define f(n,i,a) = sum_{k=0..n-i} (binomial(n,k)*stirling1(n-k,i)*product_{j=0..k-1} (-a-j)), then a(n-1) = -f(n,n-1,11), for n>=1. - Milan Janjic, Dec 20 2008
a(-1)=0, a(0)=11, a(1)=23, a(n)=3*a(n-1)-3*a(n-2)+a (n-3). - Harvey P. Dale, May 01 2016
Sum_{n>=0} 1/a(n) = 2*A001008(21)/(21*A002805(21)) = 18858053/54318264.
Sum_{n>=0} (-1)^n/a(n) = 4*log(2)/21 - 166770367/2444321880. (End)
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EXAMPLE
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G.f. = 11 + 23*x + 36*x^2 + 50*x^3 + 65*x^4 + 81*x^5 + 98*x^6 + 116*x^7 + ...
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MATHEMATICA
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Join[{0}, CoefficientList[Series[(11-10x)/(1-x)^3, {x, 0, 50}], x]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 11, 23}, 60] (* Harvey P. Dale, May 01 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
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EXTENSIONS
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STATUS
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approved
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