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A246951 Number of endofunctions f on [n] such that the number of cycles of f is a multiple of 3 for each size that is a multiple of 3.

%I A246951 #6 Sep 10 2014 20:35:38
%S A246951 1,1,4,25,224,2625,37936,651553,12963840,293219361,7429984000,
%T A246951 208486630121,6417388432896,214990745268065,7787303908091904,
%U A246951 303250854519320625,12633932936000045056,560712315504995304897,26410168773292930375680,1315770870814835066545081
%N A246951 Number of endofunctions f on [n] such that the number of cycles of f is a multiple of 3 for each size that is a multiple of 3.
%H A246951 Alois P. Heinz, <a href="/A246951/b246951.txt">Table of n, a(n) for n = 0..380</a>
%p A246951 with(combinat):
%p A246951 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246951       add(`if`(irem(j, igcd(i, 3))<>0, 0, b(n-i*j, i-1)*
%p A246951       (i-1)!^j*multinomial(n, n-i*j, i$j)/j!), j=0..n/i)))
%p A246951     end:
%p A246951 a:= n-> add(b(j$2)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A246951 seq(a(n), n=0..25);
%Y A246951 Cf. A212599.
%K A246951 nonn
%O A246951 0,3
%A A246951 _Alois P. Heinz_, Sep 08 2014