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 A074742 a(n) = (n^3 + 6n^2 - n + 12)/6. 3
 2, 3, 7, 15, 28, 47, 73, 107, 150, 203, 267, 343, 432, 535, 653, 787, 938, 1107, 1295, 1503, 1732, 1983, 2257, 2555, 2878, 3227, 3603, 4007, 4440, 4903, 5397, 5923, 6482, 7075, 7703, 8367, 9068, 9807, 10585, 11403, 12262, 13163, 14107, 15095, 16128, 17207, 18333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES A. Schultze, Advanced Algebra, Macmillan, London, 1910; p. 552. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA From R. J. Mathar, Sep 23 2008: (Start) G.f.: (2 - 5*x + 7*x^2 - 3*x^3)/(1-x)^4. a(n) = A027965(n+1), n > 0. (End) E.g.f.: exp(x)*(12 + 6*x + 9*x^2 + x^3)/6. - Stefano Spezia, Jul 12 2023 MATHEMATICA Table[(n^3 + 6n^2 - n + 12)/6, {n, 0, 49}] (* Alonso del Arte, Jan 13 2012 *) CoefficientList[Series[(2-5x+7x^2-3x^3)/(1-x)^4, {x, 0, 50}], x] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {2, 3, 7, 15}, 50] (* Harvey P. Dale, Aug 05 2022 *) PROG (PARI) a(n)=n*(n^2+6*n-1)/6+2 \\ Charles R Greathouse IV, Jan 13 2012 (Magma) [(n^3 + 6*n^2 - n + 12)/6: n in [0..50]]; // Vincenzo Librandi, Jan 13 2012 CROSSREFS Cf. A027965. Sequence in context: A098763 A001276 A006884 * A020873 A049958 A298403 Adjacent sequences: A074739 A074740 A074741 * A074743 A074744 A074745 KEYWORD nonn,easy AUTHOR Susanna Cuyler, Sep 06 2002 STATUS approved

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Last modified September 22 18:10 EDT 2023. Contains 365531 sequences. (Running on oeis4.)