A365246 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^2*A(x)^4).
1, 1, 2, 6, 22, 88, 370, 1613, 7230, 33117, 154330, 729369, 3487470, 16840346, 82007012, 402269702, 1985867630, 9858739759, 49187798158, 246506563980, 1240337033398, 6263601365616, 31734939452116, 161270637750264, 821802841072422, 4198348868249768
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, binomial(n-k-1, k)*binomial(2*n+1, n-2*k))/(2*n+1);
Formula
a(n) = (1/(2*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k-1,k) * binomial(2*n+1,n-2*k).