A375697 - OEIS

%I #8 Aug 25 2024 09:58:08

%S 1,0,4,6,128,610,11712,107114,2167776,30285378,678296720,12761459722,

%T 321364284144,7550564959106,214210299545088,5993932335381930,

%U 190756625697021632,6161493279498219394,218469987108304908336,7972839360644407925258

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

%F a(n) = n! * Sum_{k=0..floor(n/2)} (Product_{j=0..k-1} (3*j+2)) * Stirling2(n-k,k)/(n-k)!.

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

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

%Y Cf. A367881, A375696.

%Y Cf. A375689.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 24 2024