A379846 - OEIS

%I #7 Jan 04 2025 07:32:37

%S 1,2,15,202,3993,104896,3449431,136490768,6319722513,335372124160,

%T 20074806151551,1338341234648320,98356732036224745,

%U 7900673166769620992,688709957632464564231,64754459774124307019776,6532479591772426224737697,703834470938326183482621952

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

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

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

%Y Cf. A379456, A379847.

%Y Cf. A366232, A379701.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 04 2025