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a(n) = N(7,n) , where N(7,x) is the 7th Narayana polynomial.
G. C. Greubel, <a href="/A090200/b090200.txt">Table of n, a(n) for n = 0..1000</a>
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.
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
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
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
(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
(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
(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
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G.f.: (1+422*x+1297*x^2-908*x^3-173*x^4+8586*x^5-5*x^6)/(1-x)^7. - Philippe Deléham, Apr 03 2013; corrected by _Georg Fischer_, May 02 2019
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