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%I #48 Jan 05 2023 05:15:51
%S 1,1,10,207,6620,288040,15891234,1063219640,83665143176,7572321823536,
%T 775010639465040,88510236140283672,11158965455394331992,
%U 1539441941412714237912,230675631266761375815288,37309025609545822539225240,6478248637390494598048444224
%N E.g.f. satisfies: A(x) = 1/(1 - x * A(x)^3)^A(x).
%H Sidney Cadot, <a href="/A356960/b356960.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = Sum_{k=0..n} (3*n+k+1)^(k-1) * |Stirling1(n,k)|.
%t a[n_] := Sum[(3*n + k + 1)^(k - 1)*Abs[StirlingS1[n, k]], {k, 0, n}] (* _Sidney Cadot_, Jan 05 2023 *)
%o (PARI) a(n) = sum(k=0, n, (3*n+k+1)^(k-1)*abs(stirling(n, k, 1)));
%Y Cf. A052813, A349556, A356914.
%Y Cf. A356973.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 07 2022