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 A004282 n*(n+1)^2*(n+2)^2/12. 2

%I

%S 0,3,24,100,300,735,1568,3024,5400,9075,14520,22308,33124,47775,67200,

%T 92480,124848,165699,216600,279300,355740,448063,558624,690000,845000,

%U 1026675,1238328,1483524,1766100,2090175

%N n*(n+1)^2*(n+2)^2/12.

%H Vincenzo Librandi, <a href="/A004282/b004282.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F C(3+n, 2)*C(3+n, 3). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 10 2006

%F a(n-1) = sum {1 <= x_1, x_2 <= n} x_1*(det V(x_1,x_2))^2 = sum {1 <= i,j <= n} i*(i-j)^2, where V(x_1,x_2) is the Vandermonde matrix of order 2. - _Peter Bala_, Sep 21 2007

%F G.f.: x*(3+6*x+x^2)/(1-x)^6. [Colin Barker, Feb 09 2012]

%p [seq(numbperm (n,2)*numbperm (n,3)/12, n=2..31)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007

%p a:=n->sum(sum((n^3-n^2)/12, j=0..n),k=0..n): seq(a(n), n=1..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007

%p a:=n->(sum((numbcomp(n,4)*numbcomp(n,2)), j=3..n)):seq(a(n), n=2..39); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]

%t Table[n*(n+1)^2*(n+2)^2/12,{n,0,40} (* Vincenzo Librandi, Feb 09 2012 *)

%o (MAGMA) [n*(n+1)^2*(n+2)^2/12: n in [0..50]]; // Vincenzo Librandi, Feb 09 2012

%o (PARI) binomial(n+3,2)*binomial(n+3,3) \\ _Charles R Greathouse IV_, Feb 09 2012

%Y Cf. A006542, A107891, A114242.

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_.

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