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%I #9 Nov 10 2023 04:00:22
%S 1,1,7,107,2528,81324,3317958,164182458,9555617008,639681044040,
%T 48424744784136,4090543382765520,381452559291894864,
%U 38923292146836546864,4313976527840736485280,516083186352589573976208,66281598254535375499398144,9096262997259437367544137984
%N E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x*A(x)).
%F a(n) = Sum_{k=0..n} (n+3*k)!/(n+2*k+1)! * Stirling1(n,k).
%t Table[Sum[(n+3*k)!/(n+2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 10 2023 *)
%o (PARI) a(n) = sum(k=0, n, (n+3*k)!/(n+2*k+1)!*stirling(n, k, 1));
%Y Cf. A367156.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 07 2023