A371669 G.f. satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x))^2/2.
1, 2, 16, 178, 2300, 32380, 481932, 7458370, 118809868, 1935217180, 32083715344, 539615356884, 9184652815816, 157908543871712, 2738272978314500, 47837620415491554, 841151610003847564, 14874918252400486060, 264381545177102073600, 4720297172922980155740
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, sum(k=0, (n-1)\2, 2^(n-2*k)*binomial(n, k)*binomial(4*n-k, n-1-2*k))/n);
Formula
a(n) = (1/n) * Sum_{k=0..floor((n-1)/2)} 2^(n-2*k) * binomial(n,k) * binomial(4*n-k,n-1-2*k) for n > 0.