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 A080275 a(n)=(-1)^n(1 - (1/12)n(n + 1)(12 - n + n^2)). 0
 1, 1, -6, 17, -39, 79, -146, 251, -407, 629, -934, 1341, -1871, 2547, -3394, 4439, -5711, 7241, -9062, 11209, -13719, 16631, -19986, 23827, -28199, 33149, -38726, 44981, -51967, 59739, -68354, 77871, -88351, 99857, -112454, 126209, -141191, 157471, -175122, 194219, -214839, 237061, -260966 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the determinant of the n X n matrix M with M(i,i)=2i-1, M(i,j)=i+j. LINKS Table of n, a(n) for n=0..42. Index entries for linear recurrences with constant coefficients, signature (-5,-10,-10,-5,-1). FORMULA G.f.: (1 + 6x + 9x^2 + 7x^3 + x^4)/(1 + x)^5. a(n) = (-1)^n * (1 - A002378(n) - A002415(n)). MATHEMATICA CoefficientList[Series[(1 + 6x + 9x^2 + 7x^3 + x^4)/(1 + x)^5, {x, 0, 50}], x] LinearRecurrence[{-5, -10, -10, -5, -1}, {1, 1, -6, 17, -39}, 50] (* Harvey P. Dale, Jun 16 2023 *) CROSSREFS Cf. A002378, A002415. Sequence in context: A004799 A085278 A366104 * A061349 A213780 A101945 Adjacent sequences: A080272 A080273 A080274 * A080276 A080277 A080278 KEYWORD easy,sign AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Feb 12 2003 STATUS approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)