A336009 a(0) = ... = a(3) = 1; a(n) = Sum_{k=0..n-4} binomial(n-4,k) * a(k) * a(n-k-4).

1, 1, 1, 1, 1, 2, 4, 8, 16, 34, 82, 226, 678, 2108, 6892, 23948, 88532, 344816, 1401200, 5925000, 26146360, 120743496, 582606552, 2926675112, 15259183112, 82458502624, 461577781968, 2674216518016, 16013654472352, 98968416103968, 630595248710144

Offset

0,6

Comments

Shifts 4 places left when e.g.f. is squared.

Links

Table of n, a(n) for n=0..30.

Formula

E.g.f. A(x) satisfies: A(x) = 1 + x + x^2/2 + x^3/6 + Integral( Integral( Integral( Integral A(x)^2 dx) dx) dx) dx.

Mathematica

a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = Sum[Binomial[n - 4, k] a[k] a[n - k - 4], {k, 0, n - 4}]; Table[a[n], {n, 0, 30}]
nmax = 30; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + x^3/6 + Integrate[Integrate[Integrate[Integrate[A[x]^2, x], x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!

Crossrefs

Cf. A000142, A007558, A307971, A333497, A336010.

Sequence in context: A209971 A308031 A166354 * A180207 A013025 A034339

Adjacent sequences: A336006 A336007 A336008 * A336010 A336011 A336012

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 04 2020

Status

approved