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A090198
a(n) = N(5,n), where N(5,x) is the 5th Narayana polynomial.
6
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
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
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 22 2004
EXTENSIONS
Corrected by T. D. Noe, Nov 08 2006
STATUS
approved