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A132755
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a(n) = n*(n + 25)/2.
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2
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0, 13, 27, 42, 58, 75, 93, 112, 132, 153, 175, 198, 222, 247, 273, 300, 328, 357, 387, 418, 450, 483, 517, 552, 588, 625, 663, 702, 742, 783, 825, 868, 912, 957, 1003, 1050, 1098, 1147, 1197, 1248, 1300, 1353, 1407, 1462, 1518, 1575
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OFFSET
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0,2
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LINKS
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FORMULA
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Let 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) = -f(n, n-1, 13), for n>=1. - Milan Janjic, Dec 20 2008
a(0)=0, a(1)=13, a(2)=27; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Aug 09 2014
Sum_{n>=1} 1/a(n) = 2*A001008(25)/(25*A002805(25)) = 34052522467/111546435000.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/25 - 19081066231/334639305000. (End)
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MATHEMATICA
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Table[(n(n+25))/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 13, 27}, 50] (* Harvey P. Dale, Aug 09 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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