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a(n) = n*(n^4 + 30*n^3 + 395*n^2 + 2910*n + 11064)/120.
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%I #23 Jun 13 2015 00:51:16

%S 0,120,312,606,1040,1661,2526,3703,5272,7326,9972,13332,17544,22763,

%T 29162,36933,46288,57460,70704,86298,104544,125769,150326,178595,

%U 210984,247930,289900,337392,390936,451095,518466,593681,677408

%N a(n) = n*(n^4 + 30*n^3 + 395*n^2 + 2910*n + 11064)/120.

%H Colin Barker, <a href="/A090391/b090391.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = A084938(n+5, n) = Sum_{k=0..5} A090238(5, k)*binomial(n, k).

%F a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) for n>5. - _Colin Barker_, Feb 12 2015

%F G.f.: x*(71*x^4-316*x^3+534*x^2-408*x+120) / (x-1)^6. - _Colin Barker_, Feb 12 2015

%t Table[n (n^4 + 30 n^3 + 395 n^2 + 2910 n + 11064)/120, {n, 0, 40}] (* _Bruno Berselli_, Feb 12 2015 *)

%o (PARI) concat(0, Vec(x*(71*x^4-316*x^3+534*x^2-408*x+120)/(x-1)^6 + O(x^100))) \\ _Colin Barker_, Feb 12 2015

%o (PARI) vector(40, n, n--; n*(n^4+30*n^3+395*n^2+2910*n+11064)/120) \\ _Bruno Berselli_, Feb 12 2015

%Y Cf. A084938 (sixth diagonal), A090238.

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Jan 31 2004

%E Name rewritten by _Bruno Berselli_, Feb 12 2015