A363466 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^4 / (k*x^(3*k)) ).

1, 1, 1, 5, 15, 61, 240, 1019, 4387, 19462, 87649, 401077, 1856698, 8685295, 40978465, 194806667, 932141498, 4486014160, 21699575863, 105443142514, 514469464550, 2519437043753, 12379461876092, 61013509071216, 301553269618318, 1494229881209940, 7421627743464582, 36942997716584746

Offset

1,4

Links

Table of n, a(n) for n=1..28.

Mathematica

nmax = 28; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[A[x^k]^4/(k x^(3 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[f[k] f[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[d g[d + 3], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 28}]

Crossrefs

Cf. A007562, A052773, A363387, A363465, A363468.

Sequence in context: A149604 A149605 A149606 * A019045 A191678 A149607

Adjacent sequences: A363463 A363464 A363465 * A363467 A363468 A363469

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 03 2023

Status

approved