OFFSET
0,3
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 32*x^3 + 401*x^4 + 6941*x^5 + 154092*x^6 +...
The logarithmic derivative equals the series:
A'(x)/A(x) = 1/(1-x) + 3!*x/((1-x)*(1-3*x)) + 5!/2!*x^2/((1-x)*(1-3*x)*(1-5*x)) + 7!/3!*x^3/((1-x)*(1-3*x)*(1-5*x)*(1-7*x)) + 9!/4!*x^4/((1-x)*(1-3*x)*(1-5*x)*(1-7*x)*(1-9*x)) +...
Explicitly, the logarithm of the o.g.f. begins:
log(A(x)) = x + 7*x^2/2 + 85*x^3/3 + 1459*x^4/4 + 32281*x^5/5 + 873967*x^6/6 + 27981325*x^7/7 + 1034079739*x^8/8 +...
PROG
(PARI) {a(n)=polcoeff(exp(intformal(sum(m=1, n+1, (2*m-1)!/(m-1)!*x^(m-1)/prod(k=1, m, 1-(2*k-1)*x+x*O(x^n))))), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 05 2014
STATUS
approved