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A029576
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Number of permutations of an n-set containing a 9-cycle.
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 40320, 403200, 4435200, 53222400, 691891200, 9686476800, 145297152000, 2324754432000, 39520825344000, 671854030848000, 12765226586112000, 255304531722240000, 5361395166167040000, 117950693655674880000, 2712865954080522240000
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OFFSET
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0,10
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LINKS
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FORMULA
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a(n) = n!*(1 - Sum_{k=0..floor(n/9)} (-1)^k/(k!*9^k)).
a(n)/n! is asymptotic to 1-e^(-1/9).
Recurrence: a(n) = n*a(n-1), for n > 9 and n !== 0 (mod 9);
for k > 1, a(9*k) = a(9*k-1)*S(k)/S(k-1) where S(k) = 9*k*S(k-1) - (-1)^k with S(1) = 1.
(End)
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MATHEMATICA
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Table[n!*(1 - Sum[(-1)^k/(k!*9^k), {k, 0, Floor[n/9]}]), {n, 0, 25}] (* Paolo Xausa, Aug 11 2024 *)
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PROG
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(PARI) a(n) = n! * (1 - sum(k=0, floor(n/9), (-1)^k/(k!*9^k) ) ); \\ Stéphane Rézel, Nov 24 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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