A381784 G.f. A(x) satisfies A(x) = (1 + x*A(x)^4) * C(x*A(x)^2), where C(x) is the g.f. of A000108.
1, 2, 15, 153, 1799, 22969, 309479, 4331175, 62349575, 917335467, 13732751589, 208509835114, 3203279694575, 49701110565986, 777708690091907, 12258870836704797, 194475105262057575, 3102607480658510165, 49746656826517452788, 801205735002960886531, 12956005807148939155717
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(4*n+1, k)*binomial(4*n-2*k+1, n-k))/(4*n+1);
Formula
a(n) = (1/(4*n+1)) * Sum_{k=0..n} binomial(4*n+1,k) * binomial(4*n-2*k+1,n-k).