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 A090448 Fourth column (m=3) of triangle A090447. 5
 9, 96, 500, 1800, 5145, 12544, 27216, 54000, 99825, 174240, 290004, 463736, 716625, 1075200, 1572160, 2247264, 3148281, 4332000, 5865300, 7826280, 10305449, 13406976, 17250000, 21970000, 27720225, 34673184, 43022196, 52983000, 64795425, 78725120, 95065344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Table of n, a(n) for n=3..33. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA a(n) = A090447(n,3). a(n) = (n^3*(n-1)^2*(n-2)^1)/(1!*2!*3!) for n >= 3. From Colin Barker, Jan 21 2013: (Start) a(n) = (n^6-4*n^5+5*n^4-2*n^3)/12. G.f.: -x^3*(x^3+17*x^2+33*x+9)/(x-1)^7. (End) a(n) = A000330(n-1)^2 - A000292(n-1)^2. - J. M. Bergot, May 02 2014 a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, May 04 2021 From Amiram Eldar, Sep 08 2022: (Start) Sum_{n>=3} 1/a(n) = 207/4 - 9*Pi^2/2 - 6*zeta(3). Sum_{n>=3} (-1)^(n+1)/a(n) = 165/4 - Pi^2/4 - 48*log(2) - 9*zeta(3)/2. (End) MAPLE seq(mul(binomial(n, k), k=1..3), n=3..30); # Zerinvary Lajos, Dec 13 2007 MATHEMATICA a[n_] := Product[Binomial[n, k], {k, 0, 3}]; Array[a, 30, 3] (* Amiram Eldar, Sep 08 2022 *) CROSSREFS Cf. A000292, A000330, A090447. Sequence in context: A052389 A197665 A064504 * A264219 A005545 A228007 Adjacent sequences: A090445 A090446 A090447 * A090449 A090450 A090451 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Dec 23 2003 STATUS approved

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Last modified April 22 08:40 EDT 2024. Contains 371893 sequences. (Running on oeis4.)