A377391 - OEIS

%I #11 Oct 27 2024 09:24:06

%S 1,0,6,9,528,3150,157032,2060100,102770112,2276373456,120136435200,

%T 3868551141840,221493499198848,9438561453784320,592954244405195904,

%U 31417910131585330080,2173884244961012121600,137231093173511486016000,10452538023125775799541760

%N Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^3 ).

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

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

%F E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371231.

%F a(n) = 3 * n! * (3*n+2)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (3*n-k+3)! ).

%o (PARI) a(n) = 3*n!*(3*n+2)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(3*n-k+3)!));

%Y Cf. A371121, A377390.

%Y Cf. A371231, A377361.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 27 2024