A169712 The function W_n(8) (see Borwein et al. reference for definition).

1, 70, 639, 2716, 7885, 18306, 36715, 66424, 111321, 175870, 265111, 384660, 540709, 740026, 989955, 1298416, 1673905, 2125494, 2662831, 3296140, 4036221, 4894450, 5882779, 7013736, 8300425, 9756526, 11396295, 13234564, 15286741, 17568810, 20097331, 22889440

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:
seq(A169712(n), n=1..40) ; # uses W defined in A169715; R. J. Mathar, Mar 28 2012
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

Column 4 of A287316.

Cf. A287314.

Sequence in context: A234556 A183715 A104475 * A235488 A199829 A271495

Adjacent sequences: A169709 A169710 A169711 * A169713 A169714 A169715

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 17 2010

Status

approved