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1 + (9960 + (6804 + (2464 + (735 + (175 + (21 + n)*n)*n)*n)*n)*n)*n/5040.
6

%I #6 Jun 06 2013 07:12:28

%S 1,5,18,56,155,386,876,1836,3597,6655,11726,19812,32279,50948,78200,

%T 117096,171513,246297,347434,482240,659571,890054,1186340,1563380,

%U 2038725,2632851,3369510,4276108,5384111,6729480,8353136,10301456,12626801,15388077,18651330

%N 1 + (9960 + (6804 + (2464 + (735 + (175 + (21 + n)*n)*n)*n)*n)*n)*n/5040.

%H Vincenzo Librandi, <a href="/A145129/b145129.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (x^4-4*x^3+6*x^2-3*x+1) / (1-x)^8.

%p a := n-> 1+ (9960+ (6804+ (2464+ (735+ (175+ (21+ n) *n) *n) *n) *n) *n) *n/5040: seq(a(n), n=0..40);

%t CoefficientList[Series[(x^4 - 4 x^3 + 6 x^2 - 3 x + 1) / (1 - x)^8, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)

%Y 8th row of A145153. See row 8 of A145140/A145141 for rational coefficients and A145142 for 5040 * coefficients of polynomial.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Oct 03 2008