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 A299120 a(n) = (n-1)*(n-2)*(n+3)*(n+2)/12. 2
 1, 0, 0, 5, 21, 56, 120, 225, 385, 616, 936, 1365, 1925, 2640, 3536, 4641, 5985, 7600, 9520, 11781, 14421, 17480, 21000, 25025, 29601, 34776, 40600, 47125, 54405, 62496, 71456, 81345, 92225, 104160, 117216, 131461, 146965, 163800, 182040, 201761, 223041 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = n^4/12 + n^3/6 - 7n^2/12 - 2n/3 + 1 = (n-1)*(n-2)*(n+3)*(n+2)/12. . From Colin Barker, Feb 05 2018: (Start) G.f.: (1 - 5*x + 10*x^2 - 5*x^3 + x^4) / (1 - x)^5. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. (End) a(n) = A033275(n+2) for n > 1. - Georg Fischer, Oct 09 2018 From Amiram Eldar, Jan 12 2021: (Start) Sum_{n>=3} 1/a(n) = 43/150. Sum_{n>=3} (-1)^(n+1)/a(n) = 16*log(2)/5 - 154/75. (End) MAPLE seq(n^4/12+n^3/6-7*n^2/12-2*n/3+1, n=0..10^3); # Muniru A Asiru, Feb 04 2018 MATHEMATICA Rest@ CoefficientList[Series[(1 - 5 x + 10 x^2 - 5 x^3 + x^4)/(1 - x)^5, {x, 0, 41}], x] (* Michael De Vlieger, Feb 10 2018 *) f[n_] := n^4/12 + n^3/6 - 7*n^2/12 - 2*n/3 + 1; Array[f, 40, 0] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 0, 0, 5, 21}, 40] (* Robert G. Wilson v, Mar 12 2018 *) PROG (Magma) [n^4/12 + n^3/6 - 7*n^2/12 - 2*n/3 + 1: n in [0..40]]; (GAP) List([0..10^3], n->n^4/12+n^3/6-7*n^2/12-2*n/3+1); # Muniru A Asiru, Feb 04 2018 (PARI) Vec((1 - 5*x + 10*x^2 - 5*x^3 + x^4) / (1 - x)^5 + O(x^50)) \\ Colin Barker, Feb 05 2018 CROSSREFS Cf. A001263, A033275, A077415, A299146, A299198. Sequence in context: A096942 A122244 A146854 * A033275 A166464 A059859 Adjacent sequences: A299117 A299118 A299119 * A299121 A299122 A299123 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Feb 03 2018 EXTENSIONS Edited by Wolfdieter Lang, Apr 06 2018 STATUS approved

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Last modified November 30 19:14 EST 2022. Contains 358453 sequences. (Running on oeis4.)