A377687 - OEIS

%I #7 Nov 04 2024 09:08:44

%S 1,0,2,3,80,570,12744,198660,4969152,119968128,3607836480,

%T 115031711520,4163170478400,162622297300320,6952158785424384,

%U 319741032356928000,15818989359665802240,835755271882288128000,47015148988105365288960,2804276310235518168161280

%N E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)^3).

%F a(n) = n! * Sum_{k=0..floor(n/2)} (3*n-3*k)! * |Stirling1(n-k,k)|/( (n-k)! * (3*n-4*k+1)! ).

%o (PARI) a(n) = n!*sum(k=0, n\2, (3*n-3*k)!*abs(stirling(n-k, k, 1))/((n-k)!*(3*n-4*k+1)!));

%Y Cf. A371227, A377690.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 04 2024