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A090200 a(n) = N(7,n), where N(7,x) is the 7th Narayana polynomial.

%I A090200 #29 Feb 17 2021 03:56:22
%S A090200 1,429,4279,20071,65445,171481,387739,788019,1476841,2596645,4335711,
%T A090200 6936799,10706509,16025361,23358595,33267691,46422609,63614749,
%U A090200 85770631,113966295,149442421,193620169,248117739,314767651
%N A090200 a(n) = N(7,n), where N(7,x) is the 7th Narayana polynomial.
%H A090200 G. C. Greubel, <a href="/A090200/b090200.txt">Table of n, a(n) for n = 0..1000</a>
%H A090200 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A090200 a(n) = N(7, n) = Sum_{k>0} A001263(7, k)*n^(k-1) = n^6 + 21*n^5 + 105*n^4 + 175*n^3 + 105*n^2 + 21*n + 1.
%F A090200 G.f.: (1 +422*x +1297*x^2 -908*x^3 -173*x^4 +86*x^5 -5*x^6)/(1-x)^7. - _Philippe Deléham_, Apr 03 2013; corrected by _Georg Fischer_, May 02 2019
%F A090200 E.g.f.: (1 +428*x +1711*x^2 +1420*x^3 +380*x^4 +36*x^5 +x^6)*exp(x). - _G. C. Greubel_, Feb 16 2021
%p A090200 A090200:= n-> n^6+21*n^5+105*n^4+175*n^3+105*n^2+21*n+1; seq(A090200(n), n=0..30) # _G. C. Greubel_, Feb 16 2021
%t A090200 LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,429,4279,20071,65445,171481,387739},30] (* _Harvey P. Dale_, Feb 10 2019 *)
%o A090200 (PARI) a(n) = n^6+21*n^5+105*n^4+175*n^3+105*n^2+21*n+1 \\ _Charles R Greathouse IV_, Jan 17 2012
%o A090200 (Sage) [n^6+21*n^5+105*n^4+175*n^3+105*n^2+21*n+1 for n in (0..30)] # _G. C. Greubel_, Feb 16 2021
%o A090200 (Magma) [n^6+21*n^5+105*n^4+175*n^3+105*n^2+21*n+1: n in [0..30]]; // _G. C. Greubel_, Feb 16 2021
%Y A090200 Cf. A001263, A008550, A090198, A090199.
%K A090200 nonn,easy
%O A090200 0,2
%A A090200 _Philippe Deléham_, Jan 22 2004
%E A090200 Corrected by _T. D. Noe_, Nov 09 2006