A377445 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x))^2.
1, 2, 16, 226, 4678, 128728, 4437416, 184176816, 8949477600, 498611374704, 31343763192144, 2194986671431200, 169478318264408832, 14304849733469090976, 1310439414650613267552, 129495512412669053694720, 13731040497246647099309568, 1555129289690056322821075968
Offset: 0
Programs
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Mathematica
Table[2*Sum[(3*k+1)!/(2*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, (3*k+1)!/(2*k+2)!*abs(stirling(n, k, 1)));
Formula
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367158.
a(n) = 2 * Sum_{k=0..n} (3*k+1)!/(2*k+2)! * |Stirling1(n,k)|.
a(n) ~ 27 * n^(n-1) / (2^(5/2) * (exp(4/27) - 1)^(n - 1/2) * exp(23*n/27)). - Vaclav Kotesovec, Aug 27 2025