OFFSET
0,4
COMMENTS
Equals the antidiagonal sums of irregular triangle A201949.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..560
FORMULA
G.f.: A(x) = 1/(1 - x*(1+x^2)/(1+x*(1+x^2) - x*(1+x+x^2)/(1+x*(1+x+x^2) - x*(1+2*x+x^2)/(1+x*(1+2*x+x^2) - x*(1+3*x+x^2)/(1+x*(1+3*x+x^2) +...))))), a continued fraction.
G.f.: A(x) =1 + x*(1+x^2)/(G(0) - x*(1+x^2)) ; G(k)= k*x^2 + 1 + x + x^3 - x*(1+x+x^2+x*k)/G(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 28 2011
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 6*x^4 + 13*x^5 + 33*x^6 + 85*x^7 +...
where the g.f. equals the series:
A(x) = 1 + x*(1+x^2) + x^2*(1+x^2)*(1+x+x^2) + x^3*(1+x^2)*(1+x+x^2)*(1+2*x+x^2) + x^4*(1+x^2)*(1+x+x^2)*(1+2*x+x^2)*(1+3*x+x^2) +...
PROG
(PARI) {a(n)=sum(k=0, n, polcoeff(prod(j=0, n-k-1, 1+j*x+x^2), k))}
(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*prod(j=0, m-1, 1+j*x+x^2))+x*O(x^n), n)}
(PARI) {a(n)=local(CF=x+x*O(x)); for(k=1, n, CF=x*(1+(n-k)*x+x^2)/(1+x*(1+(n-k)*x+x^2)-CF)); polcoeff(1/(1-CF), n, x)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 06 2011
STATUS
approved