A276823 a(n) = 3 * [3*n]_2! / ([2*n+1]_2! * [n+1]_2!), where [n]_q! is the q-factorial.

1, 9, 1241, 2634489, 87807053113, 46414431022602681, 390913823614809035461305, 52571422826552549403006580802745, 113007269646365312407427675894837602068665, 3884802624238339577626451297006421856376970743148729

Offset: 1

Author

Vladimir Reshetnikov, Sep 18 2016

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, q-Factorial, q-Binomial Coefficient.

Crossrefs

Cf. A069777, A005329, A022166, A218449.

Programs

Maple

a:= n-> 3*mul((2^j-1), j=1..3*n)/
         (mul((2^j-1), j=1..2*n+1)*
          mul((2^j-1), j=1..n+1)):
seq(a(n), n=1..12);  # Alois P. Heinz, Sep 20 2016

Mathematica

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

Formula

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