A371545 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1+x))^2.
1, 2, 7, 36, 209, 1312, 8663, 59298, 416961, 2993790, 21857208, 161768154, 1210949944, 9152366596, 69745701746, 535304423948, 4134240993874, 32105769989714, 250551371644825, 1963871015580984, 15454014753626079, 122044659649929546, 966951068210379441
Offset: 0
Keywords
Programs
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PARI
a(n) = 2*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(4*k+2, k)/(4*k+2));
Formula
a(n) = 2 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(4*k+2,k)/(4*k+2).