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

Author

N. J. A. Sloane, Apr 17 2010

Keywords

• nonn
• easy

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).

Crossrefs

Column 4 of A287316.

Cf. A287314.

Programs

Magma

[-33*n+82*n^2-72*n^3+24*n^4: n in [1..40]]; // 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 *)

PARI

a(n)=-33*n+82*n^2-72*n^3+24*n^4 \\ Charles R Greathouse IV, Oct 21 2022

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