A385669 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(2*n+1,k) * binomial(2*n-k,n-k).
1, 12, 184, 3088, 54216, 977712, 17946384, 333571488, 6258363016, 118270099312, 2247983617584, 42929251009888, 823020113236816, 15830699744850912, 305362126902698784, 5904598544338068288, 114417320349085700616, 2221310577262416982512
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(2*n+1, k)*binomial(2*n-k, n-k));
Formula
a(n) = [x^n] (1+2*x)^(2*n+1)/(1-3*x)^(n+1).
a(n) = [x^n] 1/((1-2*x) * (1-5*x)^(n+1)).
a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(2*n+1,k).
a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(n+k,k).