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

0,3

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

Formula

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

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 *)

Prog

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

Crossrefs

Column k=2 of A279636.

Sequence in context: A265998 A203265 A355886 * A111154 A221539 A372139

Adjacent sequences: A033459 A033460 A033461 * A033463 A033464 A033465

Keyword

nonn

Author

N. J. A. Sloane

Status

approved