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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

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 *)

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

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