A376390 Expansion of e.g.f. (1/x) * Series_Reversion( x*(2 - exp(x))^3 ).
1, 3, 33, 666, 19923, 795438, 39849549, 2405748978, 170114699247, 13796351753670, 1262691211748865, 128760309960844554, 14478116911623185163, 1779761344294187865198, 237465809999666515842261, 34179385495053448088261154, 5279029838285444642785757415, 870905593631158913782753290198
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(2-exp(x))^3)/x)) -
PARI
a(n) = 3*sum(k=0, n, (3*n+k+2)!*stirling(n, k, 2))/(3*n+3)!;
Formula
E.g.f. A(x) satisfies A(x) = 1/(2 - exp(x*A(x)))^3.
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A367135.
a(n) = (3/(3*n+3)!) * Sum_{k=0..n} (3*n+k+2)! * Stirling2(n,k).