OFFSET
1,4
COMMENTS
Limit a(n)/a(n+1) = 0.705346681379806989636379706393941505260078161512292870... is a real root of 1 = Sum_{n>=1} x^(n^2).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
L.g.f.: L(x) = x + x^2/2 + x^3/3 + 5*x^4/4 + 6*x^5/5 + 7*x^6/6 + 8*x^7/7 + 13*x^8/8 + 28*x^9/9 + 36*x^10/10 +...
where
exp(L(x)) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 7*x^8 + 11*x^9 + 16*x^10 + 22*x^11 + 30*x^12 +...+ A006456(n)*x^n +...
exp(-L(x)) = 1 - x - x^4 - x^9 - x^16 - x^25 - x^36 +...+ -x^(n^2) +...
PROG
(PARI) {a(n)=n*polcoeff(-log(1-sum(r=1, sqrtint(n+1), x^(r^2)+x*O(x^n))), n)}
for(n=1, 50, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 12 2013
STATUS
approved