A333497 a(0) = a(1) = a(2) = 1; a(n) = Sum_{k=0..n-3} binomial(n-3,k) * a(k) * a(n-k-3).

1, 1, 1, 1, 2, 4, 8, 18, 48, 144, 456, 1560, 5808, 23184, 98160, 440832, 2101824, 10588608, 56104128, 312013440, 1818498816, 11082682368, 70467474816, 466680045312, 3214497245184, 22994283345408, 170573216656896, 1310482565462016, 10415453732637696

Offset

0,5

Comments

Shifts 3 places left when e.g.f. is squared.

Links

Georg Fischer, Table of n, a(n) for n = 0..500

Formula

E.g.f. A(x) satisfies: A(x) = 1 + x + x^2/2 + Integral( Integral( Integral A(x)^2 dx) dx) dx.

Mathematica

a[0] = a[1] = a[2] = 1; a[n_] := a[n] = Sum[Binomial[n - 3, k] a[k] a[n - k - 3], {k, 0, n - 3}]; Table[a[n], {n, 0, 28}]
nmax = 28; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + Integrate[Integrate[Integrate[A[x]^2, x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!

Crossrefs

Cf. A000142, A007558, A307970, A336009, A336010.

Sequence in context: A369386 A034766 A099785 * A367115 A166952 A135422

Adjacent sequences: A333494 A333495 A333496 * A333498 A333499 A333500

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 04 2020

Status

approved