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A169713 The function W_n(10) (see Borwein et al. reference for definition). 4
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 (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, Random Walk Integrals, 2010.

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 *)

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

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

AUTHOR

N. J. A. Sloane, Apr 17 2010

STATUS

approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)