The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A324354

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A324354

Total number of occurrences of 4 in the (signed) displacement sets of all permutations of [n+4] divided by 4!.
(history; published version)

#11 by Alois P. Heinz at Mon May 03 10:09:36 EDT 2021

STATUS

proposed

approved

#10 by Jean-François Alcover at Mon May 03 08:10:36 EDT 2021

STATUS

editing

proposed

#9 by Jean-François Alcover at Mon May 03 08:10:32 EDT 2021

MATHEMATICA

m = 23;

CoefficientList[(1-Exp[-x])/(1-x)^5 + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, May 03 2021 *)

STATUS

approved

editing

#8 by Alois P. Heinz at Sun Feb 24 15:02:46 EST 2019

STATUS

editing

approved

#7 by Alois P. Heinz at Sun Feb 24 15:02:44 EST 2019

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

MAPLE

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(4):

seq(a(n), n=0..23);

STATUS

approved

editing

#6 by Alois P. Heinz at Sat Feb 23 18:37:48 EST 2019

STATUS

editing

approved

#5 by Alois P. Heinz at Sat Feb 23 18:37:39 EST 2019

FORMULA

a(n) = A306234(n+2,24,4).

#4 by Alois P. Heinz at Sat Feb 23 18:37:08 EST 2019

LINKS

E.g.f.: (1-exp(-x))/(1-x)^5.

a(n) = -1/4! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+4-j)!.

a(n) = A306234(n+2,2).

Alois P. Heinz, <a href="/A324354/b324354.txt">Table of n, a(n) for n = 0..446</a>

FORMULA

E.g.f.: (1-exp(-x))/(1-x)^5.

a(n) = -1/4! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+4-j)!.

a(n) = A306234(n+2,2).

#3 by Alois P. Heinz at Sat Feb 23 18:34:53 EST 2019

NAME

Total number of occurrences of 4 in the (signed) displacement sets of all permutations of [n+4] divided by 4!.

LINKS

E.g.f.: (1-exp(-x))/(1-x)^5.

a(n) = -1/4! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+4-j)!.

a(n) = A306234(n+2,2).

CROSSREFS

Column k=4 of A324362.

Cf. A306234.

#2 by Alois P. Heinz at Sat Feb 23 18:15:19 EST 2019

NAME

allocated for Alois P. Heinz

4

DATA

0, 1, 9, 76, 679, 6576, 69299, 792926, 9812079, 130741156, 1867777339, 28494131106, 462487232519, 7959671021576, 144813873037539, 2777366346993766, 56009230972732639, 1184896664408025036, 26240470547134420619, 607133649024919944266, 14649976322598313989879

OFFSET

0,3

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Feb 23 2019

STATUS

approved

editing