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A104473 a(n) = binomial(n+2,2)*binomial(n+6,2). 1

%I

%S 15,63,168,360,675,1155,1848,2808,4095,5775,7920,10608,13923,17955,

%T 22800,28560,35343,43263,52440,63000,75075,88803,104328,121800,141375,

%U 163215,187488,214368,244035,276675,312480,351648,394383,440895,491400

%N a(n) = binomial(n+2,2)*binomial(n+6,2).

%H Vincenzo Librandi, <a href="/A104473/b104473.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (1/4)*(n+1)*(n+2)*(n+5)*(n+6).

%F a(n) = A034856(n+2)^2 - 1. - _J. M. Bergot_, Dec 14 2010

%F G.f.: -3*(x^2-4*x+5)/(x-1)^5. - _Colin Barker_, Sep 21 2012

%F a(n) = Sum_{i=1..n+1} i*(i+2)*(i+4). [_Bruno Berselli_, Apr 28 2014]

%F a(n) = A000217(n)*A000217(n+4) = 3*A033275(n+4). - _R. J. Mathar_, Nov 29 2015

%e a(0) = C(0+2,2)*C(0+6,2) = C(2,2)*C(6,2) = 1*15 = 155.

%e a(10) = C(10+2,2)*C(10+6,2) = C(12,2)*(16,2) = 66*120 = 7920.

%e a(6) = 1*3*5 + 2*4*6 + 3*5*7 + 4*6*8 + 5*7*9 + 6*8*10 + 7*9*11 = 1848. [_Bruno Berselli_, Apr 28 2014]

%t f[n_] := Binomial[n + 2, 2] Binomial[n + 6, 2]; Table[f[n], {n, 0, 27}] (* _Robert G. Wilson v_, Apr 20 2005 *)

%t CoefficientList[Series[-3 (x^2 - 4 x + 5)/(x - 1)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)

%o (PARI) a(n)=binomial(n+2,2)*binomial(n+6,2) \\ _Charles R Greathouse IV_, Jun 07 2013

%o (MAGMA) [Binomial(n+2, 2)*Binomial(n+6, 2): n in [0..50]]; // _Vincenzo Librandi_, Apr 28 2014

%Y Cf. A062264. Subsequence of A085780.

%K nonn,easy

%O 0,1

%A _Zerinvary Lajos_, Apr 18 2005

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Last modified April 3 19:43 EDT 2020. Contains 333198 sequences. (Running on oeis4.)