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A102305
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a(n) = n^2 + 2*n + 3.
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8
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6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027, 2118, 2211, 2306, 2403
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OFFSET
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1,1
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COMMENTS
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Essentially a duplicate of A059100.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = Pi * coth(sqrt(2)*Pi)/(2*sqrt(2)) - 7/12.
Sum_{n>=1} (-1)^(n+1)/a(n) = cosech(sqrt(2)*Pi)*Pi/(2*sqrt(2)) + 1/12. (End)
G.f.: (3 - 3*x + 2*x^2)/(1-x)^3.
E.g.f.: (3 + 3*x + x^2)*exp(x). (End)
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MAPLE
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MATHEMATICA
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Table[n^2+2n+3, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {6, 11, 18}, 50] (* Harvey P. Dale, Aug 05 2015 *)
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PROG
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(SageMath) [n^2+2*n+3 for n in range(1, 61)] # G. C. Greubel, Feb 03 2024
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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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