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 A090200 a(n) = N(7,n), where N(7,x) is the 7th Narayana polynomial. 7
 1, 429, 4279, 20071, 65445, 171481, 387739, 788019, 1476841, 2596645, 4335711, 6936799, 10706509, 16025361, 23358595, 33267691, 46422609, 63614749, 85770631, 113966295, 149442421, 193620169, 248117739, 314767651 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 29 22:05 EST 2023. Contains 367452 sequences. (Running on oeis4.)