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A033462 Exponential (or "EXP") transform of squares A000290.

%I A033462 #21 Dec 16 2016 10:19:56
%S A033462 1,1,5,22,125,836,6277,52396,479593,4757680,50738921,577894604,
%T A033462 6990138685,89376020800,1203182518189,16995248375116,251135780602193,
%U A033462 3871961504546624,62141329025501905,1035979079450355532,17907209511611407141,320387246623657457056,5924125441456047522005
%N A033462 Exponential (or "EXP") transform of squares A000290.
%C A033462 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 A033462 Alois P. Heinz, <a href="/A033462/b033462.txt">Table of n, a(n) for n = 0..500</a>
%F A033462 E.g.f.: exp(exp(x)*(x+x^2)).
%p A033462 a:= proc(n) option remember; `if`(n=0, 1,
%p A033462       add(binomial(n-1, j-1)*j^2*a(n-j), j=1..n))
%p A033462     end:
%p A033462 seq(a(n), n=0..25);  # _Alois P. Heinz_, Mar 30 2016
%t A033462 Range[0,20]! CoefficientList[Series[Exp[Exp[x](x+x^2)],{x,0,20}],x]
%t A033462 Table[Sum[BellY[n, k, Range[n]^2], {k, 0, n}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 09 2016 *)
%o A033462 (PARI)
%o A033462 N=33;  x='x+O('x^N);
%o A033462 egf=exp(x*(1+x)*exp(x));
%o A033462 Vec(serlaplace(egf))
%o A033462 /* _Joerg Arndt_, Sep 15 2012 */
%Y A033462 Column k=2 of A279636.
%K A033462 nonn
%O A033462 0,3
%A A033462 _N. J. A. Sloane_