OFFSET
0,4
COMMENTS
a(n) is the number of "sets of at least 2 lists". - Ron L.J. van den Burg, Nov 30 2021
FORMULA
a(n) = (n - 1)! * (LaguerreL(n - 1, 1, -1) - n) for n > 0.
a(n) = n! * [x^n] (exp(x/(1 - x)) - 1/(1 - x)).
a(n) = A000262(n) - n!.
EXAMPLE
a(3) = 7 because the sets with at least 2 ordered subsets of {1,2,3} are represented by 12|3, 21|3, 13|2, 31|2, 23|1, 32|1, 1|2|3.
MAPLE
egf := exp(x/(1 - x)) - 1/(1 - x): ser := series(egf, x, 24):
seq(n!*coeff(ser, x, n), n = 0..21);
MATHEMATICA
a[n_] := If[n == 0, 0, n! (Hypergeometric1F1[1 - n, 2, -1] - 1)];
Table[a[n], {n, 0, 21}]
PROG
(SageMath)
def gen():
a, b, c, n, f = 0, 0, 1/2, 3, 6
yield 0; yield 0; yield 1
while True:
a, b, c = b, c, ((n - 3)*a + (5 - 3*n)*b + (3*n - 2)*c) // n
yield c * f
n += 1
f *= n
a = gen(); print([next(a) for _ in range(22)])
(PARI) a(n) = if (n==0, 0, (n-1)! * (pollaguerre(n-1, 1, -1) - n)); \\ Michel Marcus, Nov 30 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 30 2021
STATUS
approved
