OFFSET
1,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..300
FORMULA
G.f. A(x) satisfies:
(1) 1 = Sum_{n>=0} x^n * ((1 + 2*x)^n - A(x))^(n+1).
(2) 1 + x = Sum_{n>=0} x^n * (1 + 2*x)^(n*(n-1)) / (1 + x*(1 + 2*x)^n*A(x))^(n+1).
FORMULA FOR TERMS.
a(n) = 1 (mod 2) for n >= 0.
EXAMPLE
G.f.: A(x) = x + 3*x^2 + 5*x^3 + 35*x^4 + 181*x^5 + 1135*x^6 + 8145*x^7 + 61839*x^8 + 509601*x^9 + 4463439*x^10 + 41334849*x^11 + 402989487*x^12 + ...
such that
1 = (1 - A(x)) + x*((1+2*x) - A(x))^2 + x^2*((1+2*x)^2 - A(x))^3 + x^3*((1+2*x)^3 - A(x))^4 + x^4*((1+2*x)^4 - A(x))^5 + x^5*((1+2*x)^5 - A(x))^6 + x^6*((1+2*x)^6 - A(x))^7 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = polcoeff( sum(m=0, #A, x^m*((1 + 2*x +x*O(x^#A))^m - x*Ser(A))^(m+1) ), #A); ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 09 2019
STATUS
approved