A276823 - OEIS

%I #10 Feb 16 2025 08:33:36

%S 1,9,1241,2634489,87807053113,46414431022602681,

%T 390913823614809035461305,52571422826552549403006580802745,

%U 113007269646365312407427675894837602068665,3884802624238339577626451297006421856376970743148729

%N a(n) = 3 * [3*n]_2! / ([2*n+1]_2! * [n+1]_2!), where [n]_q! is the q-factorial.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-Factorial.html">q-Factorial</a>, <a href="https://mathworld.wolfram.com/q-BinomialCoefficient.html">q-Binomial Coefficient</a>.

%F a(n) ~ c * 2^((n-2)*(2*n+1)), where c = 3/QPochhammer(1/2, 1/2) = 3*A065446 = 3/A048651. - _Vaclav Kotesovec_, Sep 20 2016

%p a:= n-> 3*mul((2^j-1), j=1..3*n)/

%p          (mul((2^j-1), j=1..2*n+1)*

%p           mul((2^j-1), j=1..n+1)):

%p seq(a(n), n=1..12);  # _Alois P. Heinz_, Sep 20 2016

%t Table[3 QFactorial[3 n, 2]/(QFactorial[2 n + 1, 2] QFactorial[n + 1, 2]), {n, 10}] (* or *)

%t Table[3 QBinomial[3 n, 2 n + 1, 2]/(1 - 3 * 2^n + 2^(2 n + 1)), {n, 10}]

%Y Cf. A069777, A005329, A022166, A218449.

%K nonn,changed

%O 1,2

%A _Vladimir Reshetnikov_, Sep 18 2016