A371007 - OEIS

%I #14 Nov 07 2024 15:42:02

%S 1,3,24,336,6864,185808,6286560,255703584,12163234560,662866302720,

%T 40735968170496,2787616114300416,210253334027606016,

%U 17331011952028981248,1550159522438672412672,149539908497083261980672,15476976326308703371984896

%N Expansion of e.g.f. (1/x) * Series_Reversion( 2*x/(3*exp(2*x) - 1) ).

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

%F a(n) = 1/(2*(n+1)) * Sum_{k=0..n+1} 3^k * (-1)^(n+1-k) * k^n * binomial(n+1,k).

%F a(n) = n! * Sum_{k=0..n} 3^k * 2^(n-k) * Stirling2(n,k)/(n-k+1)!. - _Seiichi Manyama_, Nov 07 2024

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(2*x/(3*exp(2*x)-1))/x))

%o (PARI) a(n) = sum(k=0, n+1, 3^k*(-1)^(n+1-k)*k^n*binomial(n+1, k))/(2*(n+1));

%Y Cf. A371005.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 08 2024