A033462 - OEIS

%I #21 Dec 16 2016 10:19:56

%S 1,1,5,22,125,836,6277,52396,479593,4757680,50738921,577894604,

%T 6990138685,89376020800,1203182518189,16995248375116,251135780602193,

%U 3871961504546624,62141329025501905,1035979079450355532,17907209511611407141,320387246623657457056,5924125441456047522005

%N Exponential (or "EXP") transform of squares A000290.

%C a(n) is the number of ways to select an ordered pair from each equivalence class in each equivalence relation on {1,2,...,n}. - _Geoffrey Critzer_, Oct 03 2011

%H Alois P. Heinz, <a href="/A033462/b033462.txt">Table of n, a(n) for n = 0..500</a>

%F E.g.f.: exp(exp(x)*(x+x^2)).

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

%p       add(binomial(n-1, j-1)*j^2*a(n-j), j=1..n))

%p     end:

%p seq(a(n), n=0..25);  # _Alois P. Heinz_, Mar 30 2016

%t Range[0,20]! CoefficientList[Series[Exp[Exp[x](x+x^2)],{x,0,20}],x]

%t Table[Sum[BellY[n, k, Range[n]^2], {k, 0, n}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 09 2016 *)

%o (PARI)

%o N=33;  x='x+O('x^N);

%o egf=exp(x*(1+x)*exp(x));

%o Vec(serlaplace(egf))

%o /* _Joerg Arndt_, Sep 15 2012 */

%Y Column k=2 of A279636.

%K nonn

%O 0,3

%A _N. J. A. Sloane_