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a(n) = Sum_{k=0..n} (3*n)!/(3*k)!.
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%I #6 Jan 27 2020 18:48:21

%S 1,7,841,423865,559501801,1527439916731,7478345832314977,

%T 59677199741873516461,724719913665311983902385,

%U 12718834484826225317486856751,309830808050366848733979830454361,10142621332336809160155563729753961697,434509897877308904421064350182659719099481

%N a(n) = Sum_{k=0..n} (3*n)!/(3*k)!.

%H Andrew Howroyd, <a href="/A087350/b087350.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = floor((3*n)!*C) where C = 1/3*exp(1)+2/3*exp(-1/2)*cos(1/2*3^(1/2)) = 1.16805831337591852551625692...

%o (PARI) a(n)={sum(k=0, n, (3*n)!/(3*k)!)} \\ _Andrew Howroyd_, Jan 27 2020

%Y Cf. A000522, A051396.

%K nonn

%O 0,2

%A _Vladeta Jovovic_, Oct 20 2003

%E Terms a(11) and beyond from _Andrew Howroyd_, Jan 27 2020