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%I #28 Jul 24 2021 18:12:56
%S 1,132,903,3304,8925,20076,39907,72528,123129,198100,305151,453432,
%T 653653,918204,1261275,1698976,2249457,2933028,3772279,4792200,
%U 6020301,7486732,9224403,11269104,13659625,16437876,19649007,23341528,27567429
%N a(n) = N(6,n), where N(6,x) is the 6th Narayana polynomial.
%H G. C. Greubel, <a href="/A090199/b090199.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) = N(6, n)= Sum_{k>0} A001263(6, k)*n^(k-1) = n^5 + 15*n^4 + 50*n^3 + 50*n^2 + 15*n + 1.
%F G.f.: (1 +126*x +126*x^2 -154*x^3 +21*x^4)/(1-x)^6. - _Philippe Deléham_, Apr 03 2013
%F E.g.f.: (1 +131*x +320*x^2 +165*x^3 +25*x^4 +x^5)*exp(x). - _G. C. Greubel_, Feb 16 2021
%t Table[(n+1)*(n^4 +14*n^3 +36*n^2 +14*n +1), {n,0,30}] (* _G. C. Greubel_, Feb 16 2021 *)
%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,132,903,3304,8925,20076},30] (* or *) CoefficientList[Series[(1+126 x+126 x^2-154 x^3+21 x^4)/(-1+x)^6,{x,0,30}],x] (* _Harvey P. Dale_, Jul 24 2021 *)
%o (PARI) a(n)=n^5+15*n^4+50*n^3+50*n^2+15*n+1 \\ _Charles R Greathouse IV_, Jan 17 2012
%o (Sage) [(n+1)*(n^4 +14*n^3 +36*n^2 +14*n +1) for n in (0..30)] # _G. C. Greubel_, Feb 16 2021
%o (Magma) [(n+1)*(n^4 +14*n^3 +36*n^2 +14*n +1): n in [0..30]]; // _G. C. Greubel_, Feb 16 2021
%Y Cf. A001263, A008550, A090198, A090200.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Jan 22 2004
%E Corrected generating function in Formula field. - _Harvey P. Dale_, Jul 24 2021