A355258 a(n) = n! * [x^n] (1 - x)*log((1 - x)/(1 - 2*x)).

0, 1, 1, 5, 34, 294, 3096, 38520, 553680, 9036720, 165191040, 3344664960, 74321452800, 1798531257600, 47088252288000, 1326311841254400, 39993302622873600, 1285497518393088000, 43878291581988864000, 1585102883250991104000, 60420385100090695680000, 2423528644964637450240000

Offset: 0

Author

Peter Luschny, Jul 01 2022

Keywords

• nonn

Crossrefs

Cf. A355257.

Programs

Maple

egf := (1 - x)*log((1 - x)/(1 - 2*x)): ser := series(egf, x, 23):
seq(n!*coeff(ser, x, n), n = 0..21);
# Alternative:
a := n -> local k; n! * ifelse(n < 2, n, (2^(n - 1)*(n - 2) + 1) / (n*(n - 1))):
seq(a(n), n = 0..21);  # Peter Luschny, Apr 12 2024

Mathematica

a[0]:=0; a[1]:=1; a[n_]:=n!*Sum[Binomial[n-2,k]/(k+2), {k,0,n-2}];
Flatten[Table[a[n],{n,0,21}]] (* Detlef Meya, Apr 12 2024 *)

Formula

For n>=2, a(n) = (1 + 2^(n-1) * (n-2)) * (n-2)!. - Vaclav Kotesovec, Jul 01 2022

For n>=2, a(n) = n!*Sum_{k, 0, n - 2} (binomial(n - 2, k)/(k + 2)). - Detlef Meya, Apr 12 2024