A377740 E.g.f. satisfies A(x) = exp(x) * (1 + x * A(x))^2.
1, 3, 19, 199, 2957, 57341, 1377175, 39531927, 1321803705, 50491876825, 2170432191491, 103726081148339, 5456983990544773, 313449393386822421, 19521567325327386831, 1310428405901227674511, 94325931842372734994417, 7248016420075574268626225, 592190617414334419733622139
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (k+1)^(n-k-1)*binomial(2*k+2, k)/(n-k)!);
Formula
E.g.f.: 4*exp(x)/(1 + sqrt(1 - 4*x*exp(x)))^2.
a(n) = n! * Sum_{k=0..n} (k+1)^(n-k-1) * binomial(2*k+2,k)/(n-k)!.
a(n) = A295238(n+1)/(n+1).