A090198 a(n) = N(5,n), where N(5,x) is the 5th Narayana polynomial.

1, 42, 197, 562, 1257, 2426, 4237, 6882, 10577, 15562, 22101, 30482, 41017, 54042, 69917, 89026, 111777, 138602, 169957, 206322, 248201, 296122, 350637, 412322, 481777, 559626, 646517, 743122, 850137, 968282, 1098301, 1240962, 1397057

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 (5,-10,10,-5,1).

Formula

a(n) = N(5, n) = Sum_{k>0} A001263(5, k)*n^(k-1) = n^4 +10*n^3 +20*n^2 +10*n +1.

G.f.: (1 +37*x -3*x^2 -13*x^3 +2*x^4)/(1-x)^5. - Philippe Deléham, Apr 03 2013

E.g.f.: (1 +41*x +57*x^2 +16*x^3 +x^4)*exp(x). - G. C. Greubel, Feb 16 2021

Maple

A090198:= n-> n^4 +10*n^3 +20*n^2 +10*n +1; seq(A090198(n), n=0..40) # G. C. Greubel, Feb 16 2021

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 42, 197, 562, 1257}, 40] (* Harvey P. Dale, Mar 06 2020 *)

Prog

(PARI) a(n) = n^4+10*n^3+20*n^2+10*n+1 \\ Charles R Greathouse IV, Jan 17 2012
(Sage) [n^4 +10*n^3 +20*n^2 +10*n +1 for n in (0..40)] # G. C. Greubel, Feb 16 2021
(Magma) [n^4 +10*n^3 +20*n^2 +10*n +1: n in [0..40]]; // G. C. Greubel, Feb 16 2021

Crossrefs

Cf. A001263, A008550, A090199, A090200.

Sequence in context: A116871 A158484 A154047 * A299056 A299817 A236278

Adjacent sequences: A090195 A090196 A090197 * A090199 A090200 A090201

Keyword

nonn,easy

Author

Philippe Deléham, Jan 22 2004

Extensions

Corrected by T. D. Noe, Nov 08 2006

Status

approved