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A090199 a(n) = N(6,n), where N(6,x) is the 6th Narayana polynomial. 6
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 (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 (6,-15,20,-15,6,-1).

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

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 *)

PROG

(PARI) a(n)=n^5+15*n^4+50*n^3+50*n^2+15*n+1 \\ Charles R Greathouse IV, Jan 17 2012

(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

(Magma) [(n+1)*(n^4 +14*n^3 +36*n^2 +14*n +1): n in [0..30]]; // G. C. Greubel, Feb 16 2021

CROSSREFS

Cf. A001263, A008550, A090198, A090200.

Sequence in context: A158543 A156958 A305271 * A239598 A033278 A213380

Adjacent sequences:  A090196 A090197 A090198 * A090200 A090201 A090202

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Jan 22 2004

EXTENSIONS

Corrected generating function in Formula field. - Harvey P. Dale, Jul 24 2021

STATUS

approved

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)