A364594 G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^4.
1, 1, 2, 4, 11, 31, 98, 316, 1065, 3649, 12775, 45299, 162713, 590097, 2159015, 7957003, 29517141, 110116277, 412879256, 1555048142, 5880591163, 22319380999, 84992915958, 324634976440, 1243396473153, 4774504667881, 18376620653851, 70883537152927
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n\2, binomial(n, 2*k)*binomial(4*k, k)/(3*k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * binomial(4*k,k) / (3*k+1).