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%I #28 Sep 08 2022 08:45:12
%S 1,14,45,100,185,306,469,680,945,1270,1661,2124,2665,3290,4005,4816,
%T 5729,6750,7885,9140,10521,12034,13685,15480,17425,19526,21789,24220,
%U 26825,29610,32581,35744,39105,42670,46445,50436,54649,59090,63765
%N a(n) = n^3 + 6*n^2 + 6*n + 1.
%C N(4,n) where N(4,x) is the 4th Narayana polynomial.
%C a(n) + A016921(n+1) = (n+2)^3. [_Bruno Berselli_, Jun 24 2012]
%H Vincenzo Librandi, <a href="/A090197/b090197.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = N(4,n) = Sum_{k>0} A001263(4, k)*n^(k-1) = (n+1)*(n^2+5*n+1).
%F G.f.: (1 + 10*x - 5*x^2) / (x-1)^4. - _R. J. Mathar_, Sep 07 2011
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 24 2012
%t LinearRecurrence[{4,-6, 4, -1},{1,14,45,100},40] (* _Vincenzo Librandi_, Jun 24 2012 *)
%o (PARI) n^3+6*n^2+6*n+1 \\ _Charles R Greathouse IV_, Jan 17 2012
%o (Magma) I:=[1, 14, 45, 100]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 24 2012
%Y For N(3,n), see A028387.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Jan 22 2004
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