A355070 - OEIS

%I #17 Jun 18 2022 13:59:44

%S 0,1,-2,28,-1808,469072,-456745472,1601325615808,-19650153075181568,

%T 826737899840505194752,-117393483573257494026125312,

%U 55564698792825562646890851908608,-86789641569440259960965030826164092928

%N G.f.: Sum_{n>=0} a(n)*x^n/(n!*3^(n*(n-1)/2)) = log( Sum_{n>=0} x^n/(n!*3^(n*(n-1)/2)) ).

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

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

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; for(i=1, n, v[i+1]=1-sum(j=1, i-1, 3^(j*(i-j))*binomial(i-1, j)*v[i-j+1])); v;

%Y Cf. A134531, A355071.

%Y Cf. A188457, A355073.

%K sign

%O 0,3

%A _Seiichi Manyama_, Jun 18 2022