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A169712 The function W_n(8) (see Borwein et al. reference for definition). 5
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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

AUTHOR

N. J. A. Sloane, Apr 17 2010

STATUS

approved

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Last modified October 3 18:24 EDT 2022. Contains 357237 sequences. (Running on oeis4.)