OFFSET
1,2
COMMENTS
Conjecture: the series exp(Sum_{n>=1} a(n)^m*x^n/n) consists entirely of integer coefficients only when m is a nonnegative even integer.
FORMULA
a(n) = sqrt( A177430(n) ).
EXAMPLE
L.g.f.: L(x) = x + 9*x^2/2 + 16*x^3/3 + 25*x^4/4 + 36*x^5/5 +...+ a(n)^2*x^n/n +...
exp(L(x)) = 1 + x + 5*x^2 + 10*x^3 + 24*x^4 + 51*x^5 + 122*x^6 + 244*x^7 +...+ A177432(n)*x^n +...
PROG
(PARI) {a(n)=local(V, A=[1], M); V=Vec(exp(x+sum(k=2, n-1, a(k)^2*x^k/k)+t*x^n/n+x*O(x^n))); if(n==1, M=1, M=a(n-1); for(m=M+1, 3*M, if(denominator(subst(V[ #V], t, m^2))==1, M=m^2; break)); sqrtint(M))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 06 2010
STATUS
approved