OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..2136 (first 500 terms from Paul D. Hanna)
FORMULA
a(n) = Sum_{d|n} d*A000081(d).
L.g.f.: Sum_{n>=1} -A000081(n) * log(1-x^n).
L.g.f.: log( G(x)/x ) = Sum_{n>=1} G(x^n)/n where G(x) is the g.f. of A000081, which is the number of rooted trees with n nodes.
a(n) ~ c * d^n / sqrt(n), where d = A051491 = 2.9557652856519949747148..., c = A187770 = 0.4399240125710253040409... . - Vaclav Kotesovec, Oct 30 2014
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 19*x^4/4 + 46*x^5/5 + 129*x^6/6 +...
Let G(x) be the g.f. of A000081, then
exp(L(x)) = G(x)/x where G(x) = x*exp( Sum_{n>=1} G(x^n)/n ) begins:
G(x) = x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 20*x^6 + 48*x^7 + 115*x^8 + 286*x^9 + 719*x^10 + 1842*x^11 + 4766*x^12 + 12486*x^13 + 32973*x^14 +...
PROG
(PARI) {a(n)=local(L=vector(n, i, 1)); for(i=1, n, L=Vec(deriv(sum(m=1, n, x^m/m*exp(sum(k=1, n\m, L[k]*x^(m*k)/k)+x*O(x^n)))))); L[n]}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 07 2012
STATUS
approved