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 A319576 a(n) = (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9). 4
 0, 0, 8, 24, 48, 112, 312, 840, 2016, 4320, 8424, 15224, 25872, 41808, 64792, 96936, 140736, 199104, 275400, 373464, 497648, 652848, 844536, 1078792, 1362336, 1702560, 2107560, 2586168, 3147984, 3803408, 4563672, 5440872, 6448000, 7598976, 8908680, 10392984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = [x^5] JacobiTheta3(x)^n. a(n) = A319574(n,5). From Colin Barker, Oct 02 2018: (Start) G.f.: 8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6. a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5. (End) MAPLE a := n -> (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9): seq(a(n), n=0..41); PROG (PARI) concat([0, 0], Vec(8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6 + O(x^40))) \\ Colin Barker, Oct 02 2018 CROSSREFS A000012 (m=0), A005843 (m=1), A046092 (m=2), A130809 (m=3), A319575 (m=4), this sequence (m=5), A319577 (m=6). Cf. A319574. Sequence in context: A179682 A033996 A146980 * A028612 A068857 A064225 Adjacent sequences:  A319573 A319574 A319575 * A319577 A319578 A319580 KEYWORD nonn,easy AUTHOR Peter Luschny, Oct 01 2018 STATUS approved

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Last modified August 25 03:10 EDT 2019. Contains 326318 sequences. (Running on oeis4.)