A358491 a(n) = n!*Sum_{m=0..floor((n-1)/2)} 1/(n-m)/binomial(n-m-1,m).

1, 1, 5, 10, 74, 216, 2316, 8688, 128880, 581760, 11406240, 59667840, 1482693120, 8782905600, 266800262400, 1762116249600, 63536485017600, 462613126348800, 19342202181120000, 153884245616640000, 7325057766297600000

Offset: 1

Author

Vladimir Kruchinin, Nov 19 2022

Keywords

• nonn

Crossrefs

Cf. A000045, A358446

Programs

Maxima

a(n):=n!*sum(1/(n-m)/(binomial(n-m-1,m)),m,0,floor((n-1)/2));
a(n):=n!*sum((fib(i))/(n-i+1)*(2*(-1)^(i+1)+(-1)^(n)),i,1,n);

Formula

E.g.f.: log((x-1)^2*(x+1))/(x^2-x-1).

a(n) = n!*Sum_{i=1..n} (F(i)/(n-i+1))*(2*(-1)^(i+1)+(-1)^n), F(n) - Fibonacci numbers.