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A349781 a(n) = n! * (hypergeom([1 - n], [2], -1]) - 1) for n >= 1 and a(0) = 0. 0
0, 0, 1, 7, 49, 381, 3331, 32593, 354033, 4233673, 55312291, 784156341, 11991160633, 196749380413, 3447839233203, 64266128818921, 1269511428781921, 26490929023150353, 582231094609675843, 13442728593179726173, 325265025877909014441, 8230062097594150286341 (list; graph; refs; listen; history; text; internal format)
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: A344251 A333515 A324353 * A199554 A343583 A221462

Adjacent sequences: A349778 A349779 A349780 * A349782 A349783 A349784

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 30 2021

STATUS

approved

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Last modified January 28 19:04 EST 2023. Contains 359905 sequences. (Running on oeis4.)