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

1, 429, 4279, 20071, 65445, 171481, 387739, 788019, 1476841, 2596645, 4335711, 6936799, 10706509, 16025361, 23358595, 33267691, 46422609, 63614749, 85770631, 113966295, 149442421, 193620169, 248117739, 314767651

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

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

Maple

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

Mathematica

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 429, 4279, 20071, 65445, 171481, 387739}, 30] (* Harvey P. Dale, Feb 10 2019 *)

Prog

(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

Crossrefs

Cf. A001263, A008550, A090198, A090199.

Sequence in context: A064061 A244104 A115133 * A033279 A145056 A064304

Adjacent sequences: A090197 A090198 A090199 * A090201 A090202 A090203

Keyword

nonn,easy

Author

Philippe Deléham, Jan 22 2004

Extensions

Corrected by T. D. Noe, Nov 09 2006

Status

approved