A375588 - OEIS

%I #10 Aug 20 2024 09:14:13

%S 1,0,0,6,0,60,720,840,40320,378000,2116800,60207840,598752000,

%T 7792424640,181863601920,2288689603200,45855781171200,

%U 1016682053587200,17113328962329600,422970486434496000,9765438564930048000,213305542403822668800,5916931500898517299200

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))))

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

%Y Cf. A052848, A375589.

%Y Cf. A357966, A375561.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Aug 19 2024