OFFSET
1,2
FORMULA
a(n) = 1 + n*Sum_{k=1..[n/2]} C(n-k,k)*a(n-k)^k/(n-k) for n>1 with a(1)=1.
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 59*x^4/4 + 796*x^5/5 +...
L(x) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+10*x)^3*x^3/3 + (1+59*x)^4*x^4/4 +...
exp(L(x)) = g.f. of A158872 is an integer series:
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 20*x^4 + 182*x^5 + 6552*x^6 +...
MATHEMATICA
nmax = 15; a = ConstantArray[0, nmax]; a[[1]] = 1; Do[a[[n]] = 1 + n*Sum[Binomial[n-k, k]/(n-k) * a[[n-k]]^k, {k, 1, Floor[n/2]}], {n, 2, nmax}]; a (* Vaclav Kotesovec, Mar 07 2014 *)
PROG
(PARI) {a(n)=1+n*sum(k=1, n\2, binomial(n-k, k)*a(n-k)^k/(n-k))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 10 2009
STATUS
approved