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 A341768 a(n) = n * (binomial(n,2) - 2). 0
 0, -2, -2, 3, 16, 40, 78, 133, 208, 306, 430, 583, 768, 988, 1246, 1545, 1888, 2278, 2718, 3211, 3760, 4368, 5038, 5773, 6576, 7450, 8398, 9423, 10528, 11716, 12990, 14353, 15808, 17358, 19006, 20755, 22608, 24568, 26638, 28821, 31120, 33538, 36078, 38743, 41536, 44460 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The n-th second n-gonal number. LINKS Table of n, a(n) for n=0..45. Index to sequences related to polygonal numbers Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: -x*(2 - 6*x + x^2)/(1 - x)^4. E.g.f.: -exp(x)*x*(4 - 2*x - x^2)/2. a(n) = n^2*(n - 1)/2 - 2*n. EXAMPLE a(7) = A147875(7) = A000566(-7) = 133. MATHEMATICA Table[n (Binomial[n, 2] - 2), {n, 0, 45}] LinearRecurrence[{4, -6, 4, -1}, {0, -2, -2, 3}, 46] CoefficientList[Series[-x (2 - 6 x + x^2)/(1 - x)^4, {x, 0, 45}], x] CROSSREFS Cf. A005449, A005564, A006002, A014105, A033954, A034856, A045944, A060354, A062728, A135705, A147875, A179986, A292551. Sequence in context: A153938 A060790 A109843 * A184840 A164022 A089751 Adjacent sequences: A341765 A341766 A341767 * A341769 A341770 A341771 KEYWORD sign,easy AUTHOR Ilya Gutkovskiy, Feb 19 2021 STATUS approved

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Last modified August 5 15:49 EDT 2024. Contains 374950 sequences. (Running on oeis4.)