OFFSET
1,7
COMMENTS
Compare to A243156, where the g.f. G(x) satisfies:
x = G(x) * (1 - G(x)) / (1 - G(x) - G(x)^3) such that G(0) = 1.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..300
FORMULA
a(n) = (1/n)*(Sum_{k=0..floor((n-1)/3)} binomial(n,k)*binomial(n-2*k-2,n-1-3*k)*(-1)^k). - Tani Akinari, May 21 2018
D-finite with recurrence -n*(n+1)*a(n) +9*n*(n-1)*a(n-1) +6*(-6*n^2+22*n-17)*a(n-2) +27*(3*n-7)*(n-4)*a(n-3) +2*(-14*n^2+172*n-435)*a(n-4) -3*(53*n-192)*(n-5)*a(n-5) +341*(n-5)*(n-6)*a(n-6)=0. - R. J. Mathar, Mar 24 2023
EXAMPLE
G.f.: A(x) = x - x^4 - x^5 - x^6 + 2*x^7 + 6*x^8 + 11*x^9 + 5*x^10 - 21*x^11 - 78*x^12 - 124*x^13 - 53*x^14 + 335*x^15 +...
wherer A(x) = x * (1 - A(x) - A(x)^3) / (1 - A(x)).
PROG
(PARI) {a(n)=local(A=x); A=serreverse(x*(1 - x)/(1 - x - x^3 +x*O(x^n))); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))
(PARI) {a(n)=sum(k=0, floor((n-1)/3), binomial(n, k)*binomial(n-2*k-2, n-1-3*k)*(-1)^k)/n} \\ Tani Akinari, May 21 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 31 2014
STATUS
approved