A354736 a(0) = a(1) = 1; a(n) = 5 * Sum_{k=0..n-2} a(k) * a(n-k-2).

1, 1, 5, 10, 55, 150, 775, 2550, 12500, 46250, 219375, 875000, 4075000, 17071250, 78796875, 341100000, 1569350000, 6947531250, 31966000000, 143761750000, 662668906250, 3014440000000, 13932834296875, 63921914062500, 296358191406250, 1368603488281250, 6365085546875000

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

G.f. A(x) satisfies: A(x) = 1 + x + 5 * (x * A(x))^2.

G.f.: (1 - sqrt(1 - 20 * x^2 * (1 + x))) / (10 * x^2).

a(n) ~ sqrt((2+3*r)*(1+r)) / (sqrt(Pi) * n^(3/2) * r^n), where r = 2*cos(arccos(-13/40)/3)/3 - 1/3. - Vaclav Kotesovec, Jun 04 2022

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = 5 Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]
nmax = 26; CoefficientList[Series[(1 - Sqrt[1 - 20 x^2 (1 + x)])/(10 x^2), {x, 0, nmax}], x]

Crossrefs

Cf. A007477, A156058, A354733, A354734, A354735.

Sequence in context: A277247 A270131 A271295 * A005438 A072309 A328332

Adjacent sequences: A354733 A354734 A354735 * A354737 A354738 A354739

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 04 2022

Status

approved