A363465 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^3 / (k*x^(2*k)) ).

1, 1, 1, 4, 10, 35, 113, 405, 1447, 5369, 20143, 76908, 296800, 1157784, 4554142, 18050308, 72003513, 288880549, 1164867528, 4718481975, 19190711729, 78338352168, 320851617424, 1318115448886, 5430133003281, 22427330328214, 92847100210382, 385217596191075, 1601483701650310

Offset: 1

Author

Ilya Gutkovskiy, Jun 03 2023

Keywords

• nonn

Crossrefs

Cf. A007562, A052751, A363387, A363466, A363467.

Programs

Mathematica

nmax = 29; A[] = 0; Do[A[x] = x + x^2 Exp[Sum[A[x^k]^3/(k x^(2 k)), {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = a[2] = 1; f[n_] := f[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; g[n_] := g[n] = Sum[a[k] f[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[d g[d + 2], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 29}]