A375562 - OEIS

%I #10 Aug 19 2024 12:14:38

%S 1,0,0,0,24,0,0,2520,40320,0,1209600,39916800,479001600,1556755200,

%T 79913433600,1961511552000,25107347865600,296406190080000,

%U 11204153985024000,263564384219136000,4284610758844416000,95795516571955200000,3345240261242880000000

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^3))))

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

%Y Cf. A052830, A375561.

%Y Cf. A353227.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Aug 19 2024