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
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).
Programs
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Magma
[n^4 +10*n^3 +20*n^2 +10*n +1: n in [0..40]]; // G. C. Greubel, Feb 16 2021
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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
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Mathematica
LinearRecurrence[{5,-10,10,-5,1},{1,42,197,562,1257},40] (* Harvey P. Dale, Mar 06 2020 *) -
PARI
a(n) = n^4+10*n^3+20*n^2+10*n+1 \\ Charles R Greathouse IV, Jan 17 2012
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Sage
[n^4 +10*n^3 +20*n^2 +10*n +1 for n in (0..40)] # G. C. Greubel, Feb 16 2021
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
Extensions
Corrected by T. D. Noe, Nov 08 2006