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 A092364 a(n) = n^2*binomial(n,2). 10
 0, 4, 27, 96, 250, 540, 1029, 1792, 2916, 4500, 6655, 9504, 13182, 17836, 23625, 30720, 39304, 49572, 61731, 76000, 92610, 111804, 133837, 158976, 187500, 219700, 255879, 296352, 341446, 391500, 446865, 507904, 574992, 648516, 728875, 816480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Coefficient of x^2 in expansion of (1+n*x)^n. For n>3, a(n) is twice the area of a triangle with vertices at points (C(n-1,3),C(n,3)), (C(n,3),C(n+1,3)), and (C(n+1,3),C(n+2,3)). - J. M. Bergot, Jun 05 2014 Also the Harary index of the n X n rook complement graph for n != 2. - Eric W. Weisstein, Sep 14 2017 LINKS Eric Weisstein's World of Mathematics, Harary Index Eric Weisstein's World of Mathematics, Rook Complement Graph Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = n^3*(n-1)/2. Equals A085540(n-1)/2. - Zerinvary Lajos, May 09 2007, corrected Mar 10 2011 G.f.: -x^2*(4+7*x+x^2) / (x-1)^5. - R. J. Mathar, Mar 10 2011 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Eric W. Weisstein, Sep 14 2017 From Amiram Eldar, May 14 2022: (Start) Sum_{n>=2} 1/a(n) = 6 - Pi^2/3 - 2*zeta(3). Sum_{n>=2} (-1)^n/a(n) = Pi^2/6 + 4*log(2) + 3*zeta(3)/2 - 6. (End) MAPLE A092364 := proc(n) n^3*(n-1)/2 ; end proc: # R. J. Mathar, Mar 10 2011 MATHEMATICA f[n_]:=(n^4-n^3)/2; lst={}; Do[AppendTo[lst, f[n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 04 2009 *) Table[n^2 Binomial[n, 2], {n, 20}] (* Eric W. Weisstein, Sep 14 2017 *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 4, 27, 96, 250}, 20] (* Eric W. Weisstein, Sep 14 2017 *) CoefficientList[Series[-((x (4 + 7 x + x^2))/(-1 + x)^5), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 14 2017 *) PROG (PARI) z(n)=n^2*binomial(n, 2); for(i=1, 40, print1(", "z(i))) (Magma) [n^3*(n-1)/2: n in [1..50]]; // Wesley Ivan Hurt, Jun 04 2014 CROSSREFS Cf. A085540. Sequence in context: A220019 A225902 A071174 * A296316 A071175 A352331 Adjacent sequences:  A092361 A092362 A092363 * A092365 A092366 A092367 KEYWORD nonn,easy,changed AUTHOR Jon Perry, Mar 19 2004 STATUS approved

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Last modified May 26 20:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)