OFFSET
0,3
COMMENTS
Image of C(n+1,2) under the Riordan array (1, x*(1-x)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-6,7,-6,3,-1).
FORMULA
a(n) = 3*a(n-1) - 6*a(n-2) + 7*a(n-3) - 6*a(n-4) + 3*a(n-5) - a(n-6).
a(n) = Sum_{k=0..n} binomial(k, n-k)(-1)^(n-k)*k(k+1)/2.
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)(-1)^k*(n-k)(n-k+1)/2.
a(3*n) = 0, a(3*n-2) = n*(3*n - 1)/2, a(3*n-1) = n*(3*n + 1)/2. - Ralf Stephan, May 20 2007
a(n) = ((Sum_{k=1..n+1} k^5) mod (Sum_{k=1..n+1} k^3))/((n+1)*(n+2))*(-1)^floor((n mod 6)/4). - Gary Detlefs, Oct 31 2011
MAPLE
S:=(j, n)->sum(k^j, k=1..n):seq((S(5, n+1)mod S(3, n+1))/((n+1)*(n+2))*(-1)^floor((n mod 6)/4), n=1..40). # Gary Detlefs, Oct 31 2011
MATHEMATICA
CoefficientList[Series[x*(1-x)/(1-x+x^2)^3, {x, 0, 60}], x] (* Harvey P. Dale, Apr 13 2011 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); [0] cat Coefficients(R!( x*(1-x)/(1-x+x^2)^3 )); // G. C. Greubel, Jan 01 2023
(Sage)
def A104555_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1-x)/(1-x+x^2)^3 ).list()
A104555_list(60) # G. C. Greubel, Jan 01 2023
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 14 2005
STATUS
approved