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E.g.f. satisfies A(x) = 1 / (2 - exp(x * A(x)^(1/3)))^3.
2

%I #10 Sep 02 2024 08:38:12

%S 1,3,21,234,3627,72498,1780953,52013118,1762754655,68060512458,

%T 2950869169125,142006584810918,7513205987292243,433548334132153698,

%U 27102592662130603857,1824854382978573444174,131676307468686605671623,10137713081262046098901050

%N E.g.f. satisfies A(x) = 1 / (2 - exp(x * A(x)^(1/3)))^3.

%F E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052894.

%F E.g.f.: A(x) = ( (1/x) * Series_Reversion(x * (2 - exp(x))) )^3.

%F a(n) = (3/(n+3)!) * Sum_{k=0..n} (n+k+2)! * Stirling2(n,k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(2-exp(x)))/x)^3))

%o (PARI) a(n) = 3*sum(k=0, n, (n+k+2)!*stirling(n, k, 2))/(n+3)!;

%Y Cf. A052894, A375897.

%Y Cf. A226515.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 01 2024