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%I #23 Apr 05 2024 11:07:04
%S 1,252,4653,31504,127905,384156,948157,2039808,3965409,7132060,
%T 12062061,19407312,29963713,44685564,64699965,91321216,126065217,
%U 170663868,227079469,297519120,384449121,490609372,619027773,773034624,956277025,1172733276
%N The function W_n(10) (see Borwein et al. reference for definition).
%H Vincenzo Librandi, <a href="/A169713/b169713.txt">Table of n, a(n) for n = 1..1000</a>
%H Jonathan M. Borwein, Dirk Nuyens, Armin Straub and James Wan, <a href="https://www.carmamaths.org/resources/jon/walks.pdf">Some Arithmetic Properties of Short Random Walk Integrals</a>, May 2011.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = 120*n^5 - 600*n^4 + 1250*n^3 - 1225*n^2 + 456*n. - _Peter Luschny_, May 27 2017
%F G.f.: x*(1+246*x+3156*x^2+7346*x^3+3651*x^4)/(1-x)^6. - _Vincenzo Librandi_, May 28 2017
%F 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
%p A169713 := proc(n)
%p W(n,10) ;
%p end proc:
%p seq(A169713(n),n=1..20) ; # uses W() from A169715; _R. J. Mathar_, Mar 27 2012
%p a := n -> 120*n^5 - 600*n^4 + 1250*n^3 - 1225*n^2 + 456*n:
%p seq(a(n), n=1..20); # _Peter Luschny_, May 27 2017
%t 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 *)
%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,252,4653,31504,127905,384156},30] (* _Harvey P. Dale_, Aug 09 2023 *)
%o (Magma) [120*n^5-600*n^4+1250*n^3-1225*n^2+456*n: n in [1..40]]; // _Vincenzo Librandi_, May 28 2017
%o (PARI) a(n)=120*n^5-600*n^4+1250*n^3-1225*n^2+456*n \\ _Charles R Greathouse IV_, Oct 21 2022
%Y Column 5 of A287316.
%Y Cf. A287314.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Apr 17 2010
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