OFFSET
5,1
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 260, #13
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
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 = 5..1000
Index entries for linear recurrences with constant coefficients, signature (13,-67,175,-244,172,-48).
FORMULA
Limit_{n->infinity} 8*a(n)/4^n = 1. - Philippe Deléham, Feb 22 2004
G.f.: 2*x^5*(24*x^2-29*x+8) / ((x-1)^2*(2*x-1)^2*(3*x-1)*(4*x-1)). - Colin Barker, Dec 21 2012
EXAMPLE
a(5)=16 because the permutations of [5] with four sign runs are 13254, 14253, 14352, 15342, 15243, 21435, 21534, 23154, 24153, 25143, 31425, 31524, 32415, 32514, 41325, 42315 and their reversals.
MATHEMATICA
CoefficientList[Series[2 (24 x^2 - 29 x + 8)/((x - 1)^2 (2 x - 1)^2 (3 x - 1) (4 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 13 2013 *)
PROG
(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -48, 172, -244, 175, -67, 13]^(n-5)*[16; 150; 926; 4788; 22548; 100530])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by Emeric Deutsch, Feb 18 2004
STATUS
approved