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A304933 a(0) = 0, a(1) = 1 and a(n) = 2*a(n-1)/(n-1) + 16*a(n-2) for n > 1. 3

%I #17 May 22 2018 09:47:19

%S 0,1,2,18,44,310,828,5236,14744,87462,255340,1450460,4349160,23932220,

%T 73268440,393382440,1224746032,6447212294,20354432076,105417000268,

%U 336767439560,1720348748244,5552121770888,28030318314712,91271367318096,456091040311900

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

%C 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.

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

%H Seiichi Manyama, <a href="/A304933/b304933.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%Y 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).

%Y Cf. A303537.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 21 2018

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)