OFFSET
1,2
MATHEMATICA
nmax = 22; A[_] = 0; Do[A[x_] = x Exp[2 Sum[(-1)^(k + 1) A[x^k]^2/(k x^k), {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = 1; g[n_] := g[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (2/(n - 1)) Sum[Sum[(-1)^(k/d + 1) d g[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 22}]
PROG
(PARI) seq(n)=my(p=x+O(x^2)); for(n=2, n, my(m=serprec(p, x)-1); p = x*exp(-2*sum(k=1, m, (-1)^k*subst(p + O(x^(m\k+1)), x, x^k)^2/(x^k*k)))); Vec(p) \\ Andrew Howroyd, May 30 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 30 2023
STATUS
approved