OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
From Seiichi Manyama, Jun 02 2023: (Start)
A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-2*x^(k+1))^a(k).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 2^(k/d) * a(d-1) ) * a(n-k). (End)
EXAMPLE
G.f.: A(x) = 1 + 2*x + 8*x^2 + 32*x^3 + 140*x^4 + 624*x^5 + +...
log(A(x)) = 2*A(x) + 4*A(x^2)*x^2/2 + 8*A(x^3)*x^3/3 + 16*A(x^4)*x^4/4 +...
PROG
(PARI) {a(n)=my(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, x^m+x*O(x^n))*2^m*x^m/m))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 15 2010
STATUS
approved