A382015 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.
1, 1, 3, 31, 589, 16121, 574621, 25206595, 1312188249, 79030103185, 5404390242841, 413597889825011, 35018686148243029, 3249772250267517001, 327996955065621786309, 35769289851588288786211, 4191277822883571632163121, 525144087149768803822788257, 70060367710090279786176259633
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, n!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(n+2*k, k)/((n+2*k)*(n-k-1)!)));
Formula
a(n) = n! * Sum_{k=0..n-1} (k+1)^(n-k-1) * binomial(n+2*k,k)/((n+2*k) * (n-k-1)!) for n > 0.