A090199 a(n) = N(6,n), where N(6,x) is the 6th Narayana polynomial.
1, 132, 903, 3304, 8925, 20076, 39907, 72528, 123129, 198100, 305151, 453432, 653653, 918204, 1261275, 1698976, 2249457, 2933028, 3772279, 4792200, 6020301, 7486732, 9224403, 11269104, 13659625, 16437876, 19649007, 23341528, 27567429
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Magma
[(n+1)*(n^4 +14*n^3 +36*n^2 +14*n +1): n in [0..30]]; // G. C. Greubel, Feb 16 2021
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Mathematica
Table[(n+1)*(n^4 +14*n^3 +36*n^2 +14*n +1), {n,0,30}] (* G. C. Greubel, Feb 16 2021 *) 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 *) -
PARI
a(n)=n^5+15*n^4+50*n^3+50*n^2+15*n+1 \\ Charles R Greathouse IV, Jan 17 2012
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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
Formula
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.
G.f.: (1 +126*x +126*x^2 -154*x^3 +21*x^4)/(1-x)^6. - Philippe Deléham, Apr 03 2013
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
Extensions
Corrected generating function in Formula field. - Harvey P. Dale, Jul 24 2021