A370909 - OEIS

%I #8 Mar 05 2024 09:07:49

%S 1,2,14,174,3174,76902,2331630,85048686,3629630070,177523551990,

%T 9793095667326,601667773414974,40747538527887366,3016185673617546822,

%U 242280567558408368142,20991011860150103490318,1951271511259385883645846,193723174296061459833879702

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

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

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

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

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

%Y Cf. A201595, A370910.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 05 2024