A349781 a(n) = n! * (hypergeom([1 - n], [2], -1) - 1) for n >= 1 and a(0) = 0.

0, 0, 1, 7, 49, 381, 3331, 32593, 354033, 4233673, 55312291, 784156341, 11991160633, 196749380413, 3447839233203, 64266128818921, 1269511428781921, 26490929023150353, 582231094609675843, 13442728593179726173, 325265025877909014441, 8230062097594150286341

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

Links

Table of n, a(n) for n=0..21.

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

Cf. A000142, A000262.

Sequence in context: A333515 A324353 A366432 * A199554 A343583 A221462

Adjacent sequences: A349778 A349779 A349780 * A349782 A349783 A349784

Keyword

nonn

Author

Peter Luschny, Nov 30 2021

Status

approved