OFFSET
0,2
COMMENTS
Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1+k*x).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..210
FORMULA
a(n) ~ sqrt(Pi) * 2^(2*n+2) * n^(2*n+3/2) / exp(2*n+1/2). - Vaclav Kotesovec, Nov 01 2014
EXAMPLE
G.f.: A(x) = 1 + 5*x + 85*x^2 + 3389*x^3 + 238021*x^4 + 25791485*x^5 +...
such that
A(x) = 1/(1+x) + 3!*x/((1+x)*(1+2*x)*(1+3*x)) + 5!*x^2/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)) + 7!*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)*(1+7*x)) + 9!*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)) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, (2*m+1)!*x^m/prod(k=1, 2*m+1, 1+k*x+x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 04 2012
STATUS
approved