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

1, 1, 5, 22, 125, 836, 6277, 52396, 479593, 4757680, 50738921, 577894604, 6990138685, 89376020800, 1203182518189, 16995248375116, 251135780602193, 3871961504546624, 62141329025501905, 1035979079450355532, 17907209511611407141, 320387246623657457056, 5924125441456047522005

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Column k=2 of A279636.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1)*j^2*a(n-j), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 30 2016

Mathematica

Range[0,20]! CoefficientList[Series[Exp[Exp[x](x+x^2)],{x,0,20}],x]
Table[Sum[BellY[n, k, Range[n]^2], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 09 2016 *)

PARI

N=33;  x='x+O('x^N);
egf=exp(x*(1+x)*exp(x));
Vec(serlaplace(egf))
/* Joerg Arndt, Sep 15 2012 */

Formula

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