A377411 E.g.f. satisfies A(x) = 1/(1 + A(x)^2 * log(1 - x))^2.
1, 2, 24, 550, 19094, 895148, 53013508, 3799302288, 319804780896, 30933514927968, 3381310375415952, 412231069711808400, 55460578942028274960, 8162361371407306334880, 1304519342283397587813600, 224999768419814742497623680, 41656460732290876726281018240
Offset: 0
Programs
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Mathematica
Table[2 * Sum[(5*k+1)!/(4*k+2)! * Abs[StirlingS1[n,k]], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Aug 27 2025 *) -
PARI
a(n) = 2*sum(k=0, n, (5*k+1)!/(4*k+2)!*abs(stirling(n, k, 1)));
Formula
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377448.
a(n) = 2 * Sum_{k=0..n} (5*k+1)!/(4*k+2)! * |Stirling1(n,k)|.
a(n) ~ 625 * n^(n-1) / (256 * (exp(256/3125) - 1)^(n - 1/2) * exp(2869*n/3125)). - Vaclav Kotesovec, Aug 27 2025