OFFSET
0,2
EXAMPLE
G.f.: A(x) = 1 + 2*x + 17*x^2 + 356*x^3 + 15050*x^4 + 1090340*x^5 +...
The logarithmic derivative equals the series:
A'(x)/A(x) = 2!/((1-x)*(1-2*x)) + 4!*x/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) + 6!*x^2/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)) + 8!*x^3/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-8*x)) + 10!*x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-8*x)*(1-9*x)*(1-10*x)) +...
Explicitly, the logarithm of the o.g.f. begins:
log(A(x)) = 2*x + 30*x^2/2 + 974*x^3/3 + 57030*x^4/4 + 5280302*x^5/5 + 710771670*x^6/6 + 131223143774*x^7/7 +...
PROG
(PARI) {a(n)=polcoeff(exp(intformal(sum(m=1, n+1, (2*m)!*x^(m-1)/prod(k=1, 2*m, 1-k*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