OFFSET
0,3
COMMENTS
Compare to an o.g.f. of Genocchi numbers of the second kind (A000366):
Sum_{n>=0} x^n * Product_{k=1..n} k*(k+1)/2 / (1 + k*(k+1)/2*x).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..260
FORMULA
a(n) ~ 2^(n+6) * n^(2*n+7/2) / (exp(2*n) * Pi^(2*n+5/2)). - Vaclav Kotesovec, Oct 28 2014
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 51*x^4 + 370*x^5 + 3691*x^6 +...
where
A(x) = 1 + x*(1+x)/(1+x) + x^2*(1+x)*(3+x)/((1+x)*(1+3*x)) + x^3*(1+x)*(3+x)*(6+x)/((1+x)*(1+3*x)*(1+6*x)) + x^4*(1+x)*(3+x)*(6+x)*(10+x)/((1+x)*(1+3*x)*(1+6*x)*(1+10*x)) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*prod(k=1, m, k*(k+1)/2+x+x*O(x^n))/prod(k=1, m, 1+k*(k+1)/2*x+x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 28 2013
STATUS
approved