A307733 a(0) = a(1) = 1; a(n) = a(n-1) + a(n-2) + Sum_{k=0..n-1} a(k) * a(n-k-1).

1, 1, 4, 14, 54, 220, 934, 4090, 18344, 83850, 389214, 1829736, 8693962, 41685714, 201442188, 980091814, 4797070022, 23603701828, 116688837886, 579312087802, 2887020896016, 14437318756818, 72424982972862, 364366674463824, 1837954750285458

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

G.f. A(x) satisfies: A(x) = (1 - x + x*A(x)^2) / (1 - x - x^2).

G.f.: (1 - x - x^2 - sqrt(1 - 6*x + 3*x^2 + 2*x^3 + x^4)) / (2*x).

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]
nmax = 24; CoefficientList[Series[(1 - x - x^2 - Sqrt[1 - 6 x + 3 x^2 + 2 x^3 + x^4])/(2 x), {x, 0, nmax}], x]

Crossrefs

Cf. A002212, A004148, A006318, A085139, A128720, A143330, A171416, A175934, A245734.

Sequence in context: A363545 A302171 A366735 * A045501 A162481 A280208

Adjacent sequences: A307730 A307731 A307732 * A307734 A307735 A307736

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 05 2020

Status

approved