OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..300
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 60*x^4/4! + 580*x^5/5! +...
such that, by definition,
A(x) = 1 + ((1+x)-1) + ((1+x)-1)*((1+x)^2-1)/2! + ((1+x)-1)*((1+x)^2-1)*((1+x)^3-1)/3! + ((1+x)-1)*((1+x)^2-1)*((1+x)^3-1)*((1+x)^4-1)/4! +...
or, more explicitly,
A(x) = 1 + x + x^2*(2+x)/2! + x^3*(2+x)*(3+3*x+x^2)/3! + x^4*(2+x)*(3+3*x+x^2)*(4+6*x+4*x^2+x^3)/4! + x^5*(2+x)*(3+3*x+x^2)*(4+6*x+4*x^2+x^3)*(5+10*x+10*x^2+5*x^3+x^4)/5! +...
PROG
(PARI) {a(n)=n!*polcoeff(sum(m=0, n, 1/m!*prod(k=1, m, (1+x)^k-1 +x*O(x^n)) ), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 19 2012
EXTENSIONS
a(21)-a(22) corrected by Andrew Howroyd, Feb 22 2018
STATUS
approved