A375696 - OEIS

%I #10 Aug 25 2024 09:58:02

%S 1,0,2,3,52,245,4206,37807,712552,9755433,207915490,3830073731,

%T 92948571420,2139142283005,58945940093782,1617324856023255,

%U 50252559901690576,1593701025177559121,55366628370374688714,1986560560083994301611

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

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

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

%Y Cf. A367881, A375697.

%Y Cf. A375688.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 24 2024