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

1,2

Links

Table of n, a(n) for n=1..22.

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}]

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, subst(p + O(x^(m\k+1)), x, x^k)^2/(x^k*k)))); Vec(p) \\ Andrew Howroyd, May 30 2023

Crossrefs

Cf. A000151, A005750, A363390.

Sequence in context: A291301 A154887 A371518 * A323842 A049671 A074609

Adjacent sequences: A363386 A363387 A363388 * A363390 A363391 A363392

Keyword

nonn

Author

Ilya Gutkovskiy, May 30 2023

Status

approved