OFFSET
0,2
COMMENTS
From Gary W. Adamson, Jul 31 2010: (Start)
Equals (1, 2, 3, 4, 5, ...) convolved with (1, 0, 3, 6, 10, 15, ...).
Example: a(4) = 36 = (5, 4, 3, 2, 1) dot (1, 0, 3, 6, 10) = (5 + 0 + 9 + 12 + 10). (End)
Also the number of permutations of length n that can be sorted by a single block interchange (in the sense of Christie). - Vincent Vatter, Aug 21 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. A. Christie, Sorting Permutations by Block-Interchanges, Inf. Process. Lett. 60 (1996), 165-169.
Cheyne Homberger, Patterns in Permutations and Involutions: A Structural and Enumerative Approach, arXiv preprint 1410.2657 [math.CO], 2014.
C. Homberger and V. Vatter, On the effective and automatic enumeration of polynomial permutation classes. [Broken link]
C. Homberger, V. Vatter, On the effective and automatic enumeration of polynomial permutation classes, arXiv preprint arXiv:1308.4946 [math.CO], 2013-2015.
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: (x^4-4*x^3+6*x^2-3*x+1) / (1-x)^5.
a(n) = C(n+3,4)+1. - Zerinvary Lajos, Mar 24 2009
MAPLE
a:= n-> 1+ (6+ (11+ (6+ n) *n) *n) *n/24: seq(a(n), n=0..40);
# second Maple program:
with(combinat): seq(binomial(n+3, 4)+1, n=0..40); # Zerinvary Lajos, Mar 24 2009
MATHEMATICA
a=b=s=0; lst={a}; Do[a+=n; b+=a; s+=b; AppendTo[lst, s], {n, 6!}]; lst+1 (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
CoefficientList[Series[(x^4 - 4 x^3 + 6 x^2 - 3 x + 1) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2013 *)
PROG
(PARI) Vec((x^4-4*x^3+6*x^2-3*x+1)/(1-x)^5 + O(x^50)) \\ Altug Alkan, Nov 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 03 2008
STATUS
approved