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E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3).
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%I #40 Nov 07 2023 09:11:10

%S 1,1,5,47,654,12084,278682,7708056,248678784,9168447600,380274659760,

%T 17524760349216,888364833282000,49125202031205936,2942774373267939168,

%U 189829708902667840320,13118899353628035596544,966975804677206274688000

%N E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3).

%C a(131) is negative. - _Vaclav Kotesovec_, Nov 07 2023

%H Vaclav Kotesovec, <a href="/A367079/b367079.txt">Table of n, a(n) for n = 0..358</a>

%F a(n) = (3*n)! * Sum_{k=0..n} Stirling1(n,k)/(3*n-k+1)!.

%t Table[(3*n)! * Sum[StirlingS1[n,k]/(3*n-k+1)!, {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 07 2023 *)

%o (PARI) a(n) = (3*n)!*sum(k=0, n, stirling(n, k, 1)/(3*n-k+1)!);

%Y Cf. A185221, A367078.

%Y Cf. A367152, A367154.

%K new,sign

%O 0,3

%A _Seiichi Manyama_, Nov 07 2023