OFFSET
0,3
COMMENTS
For a derivation of the explicit form of this sum see the link under A215308 on the partial summation formula, eq. (7).
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,3,-9,2,1).
FORMULA
O.g.f.: x*(1+x)/((1+x-x^2)*(1-4*x-x^2)*(1-x)) (from A066259).
E.g.f.: (2*exp(-x/2)*(5*cosh(sqrt(5)*x/2) + 3*sqrt(5)*sinh(sqrt(5)*x/2)) + exp(2*x)*(15*cosh(sqrt(15)*x) + 7*sqrt(5)*sinh(sqrt(5)*x)) - 25*exp(x))/50. - Stefano Spezia, Oct 28 2024
EXAMPLE
a(2) = 0 + 1^2*1 + 2^2*1 = 1 + 4 = 5.
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Wolfdieter Lang, Aug 09 2012
STATUS
approved