A169713 The function W_n(10) (see Borwein et al. reference for definition).

1, 252, 4653, 31504, 127905, 384156, 948157, 2039808, 3965409, 7132060, 12062061, 19407312, 29963713, 44685564, 64699965, 91321216, 126065217, 170663868, 227079469, 297519120, 384449121, 490609372, 619027773, 773034624, 956277025, 1172733276

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 (6,-15,20,-15,6,-1).

Formula

a(n) = 120*n^5 - 600*n^4 + 1250*n^3 - 1225*n^2 + 456*n. - Peter Luschny, May 27 2017

G.f.: x*(1+246*x+3156*x^2+7346*x^3+3651*x^4)/(1-x)^6. - Vincenzo Librandi, May 28 2017

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Vincenzo Librandi, May 28 2017

Maple

A169713 := proc(n)
        W(n, 10) ;
end proc:
seq(A169713(n), n=1..20) ; # uses W() from A169715; R. J. Mathar, Mar 27 2012
a := n -> 120*n^5 - 600*n^4 + 1250*n^3 - 1225*n^2 + 456*n:
seq(a(n), n=1..20); # Peter Luschny, May 27 2017

Mathematica

Table[120 n^5 - 600 n^4 + 1250 n^3 - 1225 n^2 + 456 n, {n, 1, 40}] (* or *) CoefficientList[Series[(1 + 246 x + 3156 x^2 + 7346 x^3 + 3651 x^4) / (1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2017 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 252, 4653, 31504, 127905, 384156}, 30] (* Harvey P. Dale, Aug 09 2023 *)

Prog

(Magma) [120*n^5-600*n^4+1250*n^3-1225*n^2+456*n: n in [1..40]]; // Vincenzo Librandi, May 28 2017
(PARI) a(n)=120*n^5-600*n^4+1250*n^3-1225*n^2+456*n \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Column 5 of A287316.

Cf. A287314.

Sequence in context: A271496 A218418 A184498 * A099059 A151610 A250085

Adjacent sequences: A169710 A169711 A169712 * A169714 A169715 A169716

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Apr 17 2010

Status

approved