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

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 3072, 9216, 27648, 82944, 248832, 746496, 2239488, 6718464, 20155392, 60466176, 241864704, 967458816, 3869835264, 15479341056, 61917364224, 247669456896, 990677827584, 3962711310336

Offset: 0

Author

Alois P. Heinz, Jul 15 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..699

Crossrefs

Column k=10 of A275062.

Cf. A010879, A059995.

Programs

Maple

f:= n -> mul(floor((n+i)/10)!,i=0..9):
map(f, [$0..30]); # Robert Israel, Jul 26 2016

Mathematica

Table[Product[Floor[(n + i)/10]!, {i, 0, 9}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 02 2018 *)

Formula

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

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

a(n) ~ (2*Pi*n)^(9/2) * n! / 10^(n + 5). - Vaclav Kotesovec, Oct 02 2018