A363389 G.f. A(x) satisfies: A(x) = x * exp(2 * Sum_{k>=1} A(x^k)^2 / (k*x^k) ).
1, 2, 11, 72, 545, 4432, 38081, 339266, 3107841, 29080910, 276786032, 2671136262, 26076724707, 257061506994, 2555287226253, 25584395476368, 257780104545994, 2611791146130284, 26593326491738879, 271972643143865548, 2792566207778712513, 28776796478486084250
Offset: 1
Keywords
Programs
-
Mathematica
nmax = 22; A[] = 0; Do[A[x] = x Exp[2 Sum[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[d g[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 22}]
-
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, subst(p + O(x^(m\k+1)), x, x^k)^2/(x^k*k)))); Vec(p) \\ Andrew Howroyd, May 30 2023