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A002626 Expansion of 1/((1-x)^3 (1-x^2)^2 (1-x^3) (1-x^4)).

%I A002626 M2727 N1094 #35 Oct 17 2023 07:22:10
%S A002626 1,3,8,17,34,61,105,170,267,403,594,851,1197,1648,2235,2981,3927,5104,
%T A002626 6565,8351,10529,13152,16303,20049,24492,29715,35841,42972,51255,
%U A002626 60813,71820,84423,98826,115203,133791,154794,178486,205104,234962,268334,305578
%N A002626 Expansion of 1/((1-x)^3 (1-x^2)^2 (1-x^3) (1-x^4)).
%D A002626 E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312.
%D A002626 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002626 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002626 Vincenzo Librandi, <a href="/A002626/b002626.txt">Table of n, a(n) for n = 0..1000</a>
%H A002626 E. Fix and J. L. Hodges, <a href="/A000601/a000601.pdf">Significance probabilities of the Wilcoxon test</a>, Annals Math. Stat., 26 (1955), 301-312. [Annotated scanned copy]
%H A002626 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=206">Encyclopedia of Combinatorial Structures 206</a>
%H A002626 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1, -4, 3, -1, 3, 0, -3, 1, -3, 4, 1, -3, 1).
%F A002626 a(n) = floor((n+1)*(n+13)*(135*(-1)^n + 2*n^4 + 56*n^3 + 570*n^2 + 2492*n + 4175)/69120 + 1/2). - _Tani Akinari_, Nov 07 2012
%t A002626 LinearRecurrence[{3, -1, -4, 3, -1, 3, 0, -3, 1, -3, 4, 1, -3, 1}, {1, 3, 8, 17, 34, 61, 105, 170, 267, 403, 594, 851, 1197, 1648}, 80] (* _Vladimir Joseph Stephan Orlovsky_, Feb 23 2012 *)
%o A002626 (PARI) Vec(1/(1-x)^3/(1-x^2)^2/(1-x^3)/(1-x^4)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 30 2012
%K A002626 nonn,easy
%O A002626 0,2
%A A002626 _N. J. A. Sloane_