|
%I #22 Sep 14 2017 16:33:48
%S 1,2,5,19,97,658,5458,53628,606871,7766312,110811174,1743359979,
%T 29972475254,558940415943,11235765584497,242168565186139,
%U 5570683131749362,136215122718876230,3527978807819506487,96480528944412962039,2778048842021042988465
%N Euler transform of numbers of preferential arrangements.
%H Alois P. Heinz, <a href="/A007003/b007003.txt">Table of n, a(n) for n = 0..160</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) ~ n! / (2*(log(2))^(n+1)). - _Vaclav Kotesovec_, Aug 25 2014
%p with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d,j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: f:= proc(n) option remember; local k; if n<=1 then 1 else add(binomial(n, k) *f(n-k), k=1..n) fi end: aa:= etr(k->f(k-1)): a:= n->aa(n+1): seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 08 2008
%t etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; b]; f[n_] := f[n] = If[n <= 1, 1, Sum[Binomial[n, k]*f[n-k], {k, 1, n}]]; aa := etr[f[#-1]&]; a[n_] := aa[n+1]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 10 2014, after _Alois P. Heinz_ *)
%Y Cf. A000670, A290352.
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Alois P. Heinz_, Sep 08 2008
|
