A002626 Expansion of 1/((1-x)^3 (1-x^2)^2 (1-x^3) (1-x^4)). (Formerly M2727 N1094)

1, 3, 8, 17, 34, 61, 105, 170, 267, 403, 594, 851, 1197, 1648, 2235, 2981, 3927, 5104, 6565, 8351, 10529, 13152, 16303, 20049, 24492, 29715, 35841, 42972, 51255, 60813, 71820, 84423, 98826, 115203, 133791, 154794, 178486, 205104, 234962, 268334, 305578

Offset

0,2

References

E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

E. Fix and J. L. Hodges, Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312. [Annotated scanned copy]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 206

Index entries for linear recurrences with constant coefficients, signature (3, -1, -4, 3, -1, 3, 0, -3, 1, -3, 4, 1, -3, 1).

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A130750 A281166 A165273 * A339011 A029859 A344004

Adjacent sequences: A002623 A002624 A002625 * A002627 A002628 A002629

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved