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 A115056 a(n) = n*(n^2-1)*(3*n+2). 2
 0, 0, 0, 48, 264, 840, 2040, 4200, 7728, 13104, 20880, 31680, 46200, 65208, 89544, 120120, 157920, 204000, 259488, 325584, 403560, 494760, 600600, 722568, 862224, 1021200, 1201200, 1404000, 1631448, 1885464, 2168040, 2481240, 2827200 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,4 REFERENCES George E. Andrews, Number Theory, Dover Publications, New York, 1971, p. 4. LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA From G. C. Greubel, Jul 17 2017: (Start) a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). G.f.: 24*x^2*(x+2)/(1-x)^5. E.g.f.: (3*x^4 + 20*x^3 + 24*x^2)*exp(x). (End) From Amiram Eldar, Mar 12 2023: (Start) Sum_{n>=2} 1/a(n) = 27*log(3)/20 - 3*sqrt(3)*Pi/20 - 16/25. Sum_{n>=2} (-1)^n/a(n) = 3*sqrt(3)*Pi/10 - 4*log(2)/5 - 53/50. (End) MATHEMATICA Table[3*n^4 + 2*n^3 - 3*n^2 - 2*n, {n, -1, 50}] (* G. C. Greubel, Jul 17 2017 *) PROG (PARI) g(n) = for(x=0, n, y=x*(x^2-1)*(3*x+2); print1(y", ")) (PARI) my(x='x+O('x^50)); concat([0, 0, 0], Vec(24*x^2*(x+2)/(1-x)^5)) \\ G. C. Greubel, Jul 17 2017 CROSSREFS Sequence in context: A235904 A275406 A205469 * A001337 A259993 A205747 Adjacent sequences: A115053 A115054 A115055 * A115057 A115058 A115059 KEYWORD nonn,easy AUTHOR Cino Hilliard, Feb 28 2006 STATUS approved

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Last modified April 18 03:33 EDT 2024. Contains 371767 sequences. (Running on oeis4.)