A377546 - OEIS

%I #10 Nov 01 2024 09:32:59

%S 1,2,18,294,7136,231410,9421932,462459242,26593896912,1754278123266,

%T 130611457831700,10835721949072922,991315043401627320,

%U 99154012317212577218,10765112531819005907484,1260860266373297376720810,158473050112495481401395872,21275613503385328981848681986

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x))^2 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364985.

%F a(n) = 2 * n! * Sum_{k=0..n} k^(n-k) * binomial(2*n+k+2,k)/( (2*n+k+2)*(n-k)! ).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x))^2)/x))

%o (PARI) a(n) = 2*n!*sum(k=0, n, k^(n-k)*binomial(2*n+k+2, k)/((2*n+k+2)*(n-k)!));

%Y Cf. A213644, A377548.

%Y Cf. A364985.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 31 2024