A363387 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^2 / (k*x^k) ).

1, 1, 1, 3, 6, 17, 42, 120, 330, 962, 2797, 8334, 24989, 75905, 232142, 715830, 2220473, 6928411, 21723883, 68424327, 216376757, 686742855, 2186771571, 6984248840, 22368127861, 71818903891, 231132440916, 745454242656, 2409080380316, 7799945417349

Offset

1,4

Links

Table of n, a(n) for n=1..30.

Mathematica

nmax = 30; A[_] = 0; Do[A[x_] = x + x^2 Exp[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] = a[2] = 1; g[n_] := g[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[d g[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 30}]

Prog

(PARI) seq(n)=my(p=x+x^2+O(x^3)); for(n=1, n\2, my(m=serprec(p, x)-1); p = x + x^2*exp(sum(k=1, m, subst(p + O(x^(m\k+1)), x, x^k)^2/(x^k*k)))); Vec(p + O(x*x^n)) \\ Andrew Howroyd, May 30 2023

Crossrefs

Cf. A005750, A007562, A363388.

Sequence in context: A121399 A212421 A238428 * A232771 A129905 A143363

Adjacent sequences: A363384 A363385 A363386 * A363388 A363389 A363390

Keyword

nonn

Author

Ilya Gutkovskiy, May 30 2023

Status

approved