A377692 E.g.f. satisfies A(x) = (1 - log(1 - x) * A(x))^2.
1, 2, 12, 118, 1634, 29408, 654040, 17362056, 536410200, 18922946928, 750902659200, 33118793900784, 1607673329621712, 85192554602094912, 4894219487974911552, 303021216528999244416, 20116223556200658052992, 1425479651299747192856832, 107400336067263661850548224
Offset: 0
Programs
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PARI
a(n) = 2*sum(k=0, n, (2*k+1)!/(k+2)!*abs(stirling(n, k, 1)));
Formula
E.g.f.: 4/(1 + sqrt(1 + 4*log(1-x)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052803.
a(n) = 2 * Sum_{k=0..n} (2*k+1)!/(k+2)! * |Stirling1(n,k)|.
a(n) ~ 2^(7/2) * n^(n-1) / ((exp(1/4) - 1)^(n - 1/2) * exp(3*n/4)). - Vaclav Kotesovec, Aug 27 2025