OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
FORMULA
G.f.: g(x) + (g(x^2) - g(x)^2)*x/(2*(1-x)) where g(x) is the g.f. of A052855.
MATHEMATICA
max = 30; g[_] = 1; Do[g[x_] = Exp[Sum[(g[x^k]/(1 - x^k))*(x^k/k) + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; CoefficientList[g[x] + (g[x^2] - g[x]^2)*(x/(2*(1 - x))) + O[x]^max, x] (* Jean-François Alcover, May 25 2018 *)
PROG
(PARI) \\ here b(n) is A052855 as series
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
b(n)={my(v=[1]); for(i=2, n, v=concat([1], v + EulerT(v))); Ser(v)*(1-x)}
seq(n)={my(g=b(n)); Vec(g + (subst(g, x, x^2) - g^2)*x/(2*(1-x)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 20 2018
STATUS
approved