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A085686
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Inverse Euler transform of Bell numbers.
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3
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1, 1, 3, 9, 34, 135, 610, 2965, 15612, 87871, 526274, 3334850, 22270254, 156172689, 1146640394, 8791424549, 70227355786, 583283741066, 5027823752930, 44903579626132, 414877600876638, 3959945232723603, 38996757506464858, 395749369598406027
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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MAPLE
| read transfoms; A := series(exp(exp(x)-1), x, 60); A000110 := n->n!*coeff(A, x, n); [seq(A000110(i), i=1..30)]; EULERi(%);
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MATHEMATICA
| n=24; eq[0] = Rest[ Thread[ CoefficientList[ 1 + Series[ Sum[ BellB[k]*x^k, {k, 1, n}] - Product[1/(1-x^k)^a[k], {k, 1, n}], {x, 0, n}], x] == 0]]; s[1] = First[ Solve[ First[eq[0]], a[1]]]; Do[eq[k] = Rest[eq[k-1]] /. s[k]; s[k+1] = First[ Solve[ First[eq[k]], a[k+1]]], {k, 1, n-1}]; Table[a[k], {k, 1, n}] /. Flatten[Table[s[k], {k, 1, n}]] (* From Jean-François Alcover, Jul 26 2011 *)
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CROSSREFS
| Cf. A000110.
Sequence in context: A149012 A145090 A137953 * A191412 A084756 A009578
Adjacent sequences: A085683 A085684 A085685 * A085687 A085688 A085689
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 18 2003
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