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<DIV>Seqfans, <BR> I don't think
I was very clear. Perhaps this is better: <BR>A(x) = 1 +
x*A(x)*B(x)<BR>B(x) = 1 + x*A(x)*B(x)*C(x)<BR>C(x) = 1 +
x*A(x)*B(x)*C(x)*D(x)<BR>D(x) = 1 + x*A(x)*B(x)*C(x)*D(x)*E(x)<BR>E(x) = 1 +
x*A(x)*B(x)*C(x)*D(x)*E(x)*F(x)<BR>...<BR>This leads to the following products:
<BR>A = 1/(1 - xB) <BR>AB = 1/(1 - xB - xC) <BR>ABC = 1/(1 - xB - xC - xD)
<BR>ABCD = 1/(1 - xB - xC - xD - xE) <BR>ABCDE = 1/(1 - xB - xC - xD - xE - xF)
<BR>...<BR>Or, equivalently, <BR>A = 1 + xB/(1 - xB) <BR>B = 1 + xC/(1 -
xB - xC) <BR>C = 1 + xD/(1 - xB - xC - xD) <BR>D = 1 + xE/(1 - xB - xC - xD -
xE) <BR>E = 1 + xF/(1 - xB - xC - xD - xE - xF) <BR>...<BR> <BR>The final
relation gives me the coefficients for A(x) to be: </DIV>
<DIV> </DIV>
<DIV>1, 1, 2, 6, 22, 93, 439, 2269, 12672, 75751, 481277, 3232126, 22843829,
<BR>169308433, 1311923063, 10600748257, 89122102396, 778020244975,
<BR>7040120987869, 65925795526266, 637943017576192, 6370573324549624,
...<BR> <BR>So, sorry, my initial calculation was incorrect! <BR>The
sequence is not found in the OEIS after all. <BR>But I thought the problem
interesting anyway. <BR> <BR>Thanks, <BR> Paul
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