A304934 a(0) = 0, a(1) = 1 and a(n) = 2*a(n-1)/(n-1) + 64*a(n-2) for n > 1.

0, 1, 2, 66, 172, 4310, 12732, 280084, 894872, 18149094, 61304940, 1173803004, 4136934888, 75812881404, 276427353048, 4891514031720, 18343552465968, 315349842088326, 1211087339244108, 20316955153568876, 79648216569893320, 1308249951485397396

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), A304933 (b=4), this sequence (b=8).

Cf. A303538.

Formula

a(n) = n*A303538(n)/2.

G.f.: x/(1-8*x)^2 * ((1-8*x)/(1+8*x))^(7/8).