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A275065 Number of permutations p of [n] such that p(i)-i is a multiple of ten for all i in [n]. 2

%I

%S 1,1,1,1,1,1,1,1,1,1,1,2,4,8,16,32,64,128,256,512,1024,3072,9216,

%T 27648,82944,248832,746496,2239488,6718464,20155392,60466176,

%U 241864704,967458816,3869835264,15479341056,61917364224,247669456896,990677827584,3962711310336

%N Number of permutations p of [n] such that p(i)-i is a multiple of ten for all i in [n].

%H Alois P. Heinz, <a href="/A275065/b275065.txt">Table of n, a(n) for n = 0..699</a>

%F a(n) = Product_{i=0..9} floor((n+i)/10)!.

%F a(n) = ((m+1)!)^10/(m+1)^(10-k) where m=floor(n/10)=A059995(n) and k=n mod 10 =A010879(n). - _Robert Israel_, Jul 26 2016

%F a(n) ~ (2*Pi*n)^(9/2) * n! / 10^(n + 5). - _Vaclav Kotesovec_, Oct 02 2018

%p f:= n -> mul(floor((n+i)/10)!,i=0..9):

%p map(f, [$0..30]); # _Robert Israel_, Jul 26 2016

%t Table[Product[Floor[(n + i)/10]!, {i, 0, 9}], {n, 0, 40}] (* _Vaclav Kotesovec_, Oct 02 2018 *)

%Y Column k=10 of A275062.

%Y Cf. A010879, A059995.

%K nonn

%O 0,12

%A _Alois P. Heinz_, Jul 15 2016

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Last modified June 22 08:36 EDT 2021. Contains 345375 sequences. (Running on oeis4.)