OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Jonathan M. Borwein, Dirk Nuyens, Armin Straub, and James Wan, Some Arithmetic Properties of Short Random Walk Integrals, May 2011.
Pakawut Jiradilok and Elchanan Mossel, Gaussian Broadcast on Grids, arXiv:2402.11990 [cs.IT], 2024. See p. 27.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = -33*n + 82*n^2 - 72*n^3 + 24*n^4. - Peter Luschny, May 27 2017
G.f.: x*(1+65*x+299*x^2+211*x^3)/(1-x)^5. - Vincenzo Librandi, May 28 2017
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Vincenzo Librandi, May 28 2017
MAPLE
A169712 := proc(n)
W(n, 8) ;
end proc:
a := n -> -33*n + 82*n^2 - 72*n^3 + 24*n^4:
seq(a(n), n=1..28); # Peter Luschny, May 27 2017
MATHEMATICA
Table[-33 n + 82 n^2 - 72 n^3 + 24 n^4, {n, 1, 40}] (* or *) CoefficientList[Series[(1 + 65 x + 299 x^2 + 211 x^3) /(1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2017 *)
PROG
(Magma) [-33*n+82*n^2-72*n^3+24*n^4: n in [1..40]]; // Vincenzo Librandi May 28 2017
(PARI) a(n)=-33*n+82*n^2-72*n^3+24*n^4 \\ Charles R Greathouse IV, Oct 21 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 17 2010
STATUS
approved
