A029577 Number of permutations of an n-set containing a 10-cycle.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 362880, 3991680, 47900160, 622702080, 8717829120, 130767436800, 2092278988800, 35568742809600, 640237370572800, 12164510040883200, 231125690776780800, 4853639506312396800, 106780069138872729600, 2455941590194072780800

Offset

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

a(n) = n! * (1 - Sum_{k=0..floor(n/10)} (-1)^k/(k!10^k));

a(n)/n! is asymptotic to 1-e^(-1/10).

E.g.f.: (1-exp(-x^10/10))/(1-x). - Alois P. Heinz, Oct 11 2017

Conjectures from Stéphane Rézel, Dec 11 2019: (Start)

Recurrence: a(n) = n*a(n-1), for n > 10 and n !== 0 (mod 10);

for k > 1, a(10*k) = a(10*k-1)*S(k)/S(k-1) where S(k) = 10*k*S(k-1) - (-1)^k with S(1) = 1.

(End)

Prog

(PARI) a(n) = n! * (1 - sum(k=0, floor(n/10), (-1)^k/(k!*10^k) ) ); \\ Stéphane Rézel, Dec 11 2019

Crossrefs

Column k=10 of A293211.

Sequence in context: A284206 A179736 A045511 * A179967 A133360 A254082

Adjacent sequences: A029574 A029575 A029576 * A029578 A029579 A029580

Keyword

nonn

Author

Rob Pratt

Status

approved