A304933 a(0) = 0, a(1) = 1 and a(n) = 2*a(n-1)/(n-1) + 16*a(n-2) for n > 1.

0, 1, 2, 18, 44, 310, 828, 5236, 14744, 87462, 255340, 1450460, 4349160, 23932220, 73268440, 393382440, 1224746032, 6447212294, 20354432076, 105417000268, 336767439560, 1720348748244, 5552121770888, 28030318314712, 91271367318096, 456091040311900

Offset: 0

Author

Seiichi Manyama, May 21 2018

Keywords

• nonn

Comments

Let a(0) = 0, a(1) = 1 and a(n) = 2*m*a(n-1)/(n-1) + k^2*a(n-2) for n > 1.

Then G.f. is x/(2*m) * d/dx ((1 + k*x)/(1 - k*x))^(m/k).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

a(n) = 2*a(n-1)/(n-1) + b^2*a(n-2): A001477 (b=1), A100071 (b=2), this sequence (b=4), A304934 (b=8).

Cf. A303537.

Formula

a(n) = n*A303537(n)/2.

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