OFFSET
0,6
COMMENTS
a(n) is odd only when n is of the form 2^k or 3*2^k, or equal to 0 (conjecture).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 8*x^7 + 17*x^8 + 48*x^9 + 128*x^10 + 380*x^11 + 1157*x^12 + 3660*x^13 + 12096*x^14 + 40792*x^15 + ...
such that
1 = 1/A(x) + x*(1+x)/A(x)^2 + x^2*(1+x)*(1+2*x)/A(x)^3 + x^3*(1+x)*(1+2*x)*(1+3*x)/A(x)^4 + x^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)/A(x)^5 + x^5*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)/A(x)^6 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=0, #A, x^m*prod(k=1, m, 1 + k*x)/Ser(A)^(m+1)), #A-1); ); A[n+1]}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 19 2019
STATUS
approved