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A019472 Weak preference orderings of n alternatives, i.e., orderings that have indifference between at least two alternatives. 1
0, 0, 1, 7, 51, 421, 3963, 42253, 505515, 6724381, 98618763, 1582715773, 27612565995, 520631327581, 10554164679243, 228975516609853, 5294731892093355, 130015079601039901, 3379132289551117323, 92679942218919579133, 2675254894236207563115, 81073734056332364441821 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

Wikipedia, Weak_ordering

FORMULA

a(n) = A000670(n) - n!. - corrected by Eugene McDonnell, May 12 2000

a(n) = Sum_{j=0..n-1} Sum_{i=0..n-1} (-1)^(j-i)*C(j, i)*i^n. - Peter Luschny, Jul 22 2014

MATHEMATICA

a[n_] := Sum[(-1)^(j-i)*Binomial[j, i]*i^n, {i, 0, n-1}, {j, 0, n-1}]; Table[a[n], {n, 0, 21}] (* Jean-Fran├žois Alcover, Feb 26 2016, after Peter Luschny *)

PROG

(Sage)

def A019472(n):

    return add(add((-1)^(j-i)*binomial(j, i)*i^n for i in range(n)) for j in range(n))

[A019472(n) for n in range(21)] # Peter Luschny, Jul 22 2014

CROSSREFS

Cf. A000670, A052875.

Sequence in context: A104454 A222849 A273055 * A219306 A246572 A230883

Adjacent sequences:  A019469 A019470 A019471 * A019473 A019474 A019475

KEYWORD

nonn,easy,nice

AUTHOR

Robert Ware (bware(AT)wam.umd.edu)

STATUS

approved

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Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)