A246530 Number of endofunctions on [n] whose cycle lengths are divisors of 10.

1, 1, 4, 25, 218, 2475, 34696, 579223, 11220540, 247395097, 6117023600, 167639670441, 5044046990776, 165322086357715, 5863394794421088, 223751099288794375, 9141963589243198736, 398198217292835137137, 18420080017512816009280, 901874615547758970425977

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Formula

E.g.f.: exp(Sum_{d|10} (-LambertW(-x))^d/d).

Maple

with(numtheory):
egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
a:= n-> n!*coeff(series(egf(10), x, n+1), x, n):
seq(a(n), n=0..25);
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*
      (i-1)!^j, j=0..`if`(irem(10, i)=0, n/i, 0))))
    end:
a:= n-> add(b(j, min(10, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Crossrefs

Column k=10 of A246522.

Sequence in context: A060912 A209319 A273996 * A268163 A050386 A246524

Adjacent sequences: A246527 A246528 A246529 * A246531 A246532 A246533

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2014

Status

approved