OFFSET
0,4
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 0, 5, 1, 1, -3, -2, 0, 1).
FORMULA
a(0)=1, a(1)=1, a(2)=1, a(3)=6, a(4)=12, a(5)=19, a(6)=48, a(7)=110, a(8)=218, a(n)=a(n-1)+5*a(n-3)+a(n-4)+a(n-5)-3*a(n-6)-2*a(n-7)+a(n-9). - Harvey P. Dale, Jan 23 2013
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 12*x^4 + 19*x^5 + 48*x^6 + 110*x^7 +...
where
log(A(x)) = x + x^2/2 + 16*x^3/3 + 25*x^4/4 + 36*x^5/5 + 100*x^6/6 + 225*x^7/7 +...+ A001609(n)^2*x^n/n +...
MATHEMATICA
CoefficientList[Series[1/((1+x^2-x^3)^2(1-x-2x^2-x^3)), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 0, 5, 1, 1, -3, -2, 0, 1}, {1, 1, 1, 6, 12, 19, 48, 110, 218}, 40] (* Harvey P. Dale, Jan 23 2013 *)
PROG
(PARI) {a(n)=polcoeff(1/((1 + x^2 - x^3)^2*(1 - x*(1+x)^2+x*O(x^n))), n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 28 2012
STATUS
approved