A261381 Number of permutations sigma of [n] without fixed points such that sigma^10 = Id.

1, 0, 1, 0, 3, 24, 15, 504, 105, 9072, 436401, 166320, 28750491, 3243240, 1307809503, 27965161224, 52309001745, 3795543015264, 2000776242465, 324424646818272, 17268536366932851, 22708075360010040, 3974396337125445231, 1436250980764880280, 548178165969608527353

Offset: 0

Author

Alois P. Heinz, Aug 17 2015

Keywords

• nonn

Examples

			a(4) = 3: 2143, 3412, 4321:
a(5) = 24: 23451, 23514, 24153, 24531, 25134, 25413, 31452, 31524, 34251, 34512, 35214, 35421, 41253, 41532, 43152, 43521, 45123, 45231, 51234, 51423, 53124, 53412, 54132, 54213.
a(6) = 15: 214365, 215634, 216543, 341265, 351624, 361542, 432165, 456123, 465132, 532614, 546213, 564312, 632541, 645231, 654321.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..490

Crossrefs

Column k=10 of A261430.

Cf. A001147, A052502, A052503, A052504, A053496, A261317.

Programs

Maple

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[2, 5, 10])))
    end:
seq(a(n), n=0..30);

Formula

E.g.f.: exp(x^2/2+x^5/5+x^10/10).