A246530 - OEIS

%I #5 Aug 28 2014 20:57:55

%S 1,1,4,25,218,2475,34696,579223,11220540,247395097,6117023600,

%T 167639670441,5044046990776,165322086357715,5863394794421088,

%U 223751099288794375,9141963589243198736,398198217292835137137,18420080017512816009280,901874615547758970425977

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

%H Alois P. Heinz, <a href="/A246530/b246530.txt">Table of n, a(n) for n = 0..350</a>

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

%p with(numtheory):

%p egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):

%p a:= n-> n!*coeff(series(egf(10), x, n+1), x, n):

%p seq(a(n), n=0..25);

%p # second Maple program:

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*

%p       (i-1)!^j, j=0..`if`(irem(10, i)=0, n/i, 0))))

%p     end:

%p a:= n-> add(b(j, min(10, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):

%p seq(a(n), n=0..25);

%Y Column k=10 of A246522.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 28 2014