A385347 Expansion of e.g.f. 1/(1 - 3 * arcsin(x)).
1, 3, 18, 165, 2016, 30807, 564912, 12085713, 295498368, 8128142667, 248419104768, 8351633349117, 306299582106624, 12169801665625887, 520721224401217536, 23872081186754865513, 1167357853571179216896, 60652216264444277244435, 3336667444310413833732096
Offset: 0
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*asin(x))))
Formula
a(n) = Sum_{k=0..n} 3^k * k! * A385343(n,k).
a(n) ~ sqrt(2*Pi) * cos(1/3) * n^(n + 1/2) / (3 * exp(n) * sin(1/3)^(n+1)). - Vaclav Kotesovec, Jun 27 2025