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A085686 Inverse Euler transform of Bell numbers. 7
1, 1, 3, 9, 34, 135, 610, 2965, 15612, 87871, 526274, 3334850, 22270254, 156172689, 1146640394, 8791424549, 70227355786, 583283741066, 5027823752930, 44903579626132, 414877600876638, 3959945232723603, 38996757506464858, 395749369598406027, 4134132167178705732 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..300

MAPLE

read transforms; A := series(exp(exp(x)-1), x, 60); A000110 := n->n!*coeff(A, x, n); [seq(A000110(i), i=1..30)]; EULERi(%);

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}]] (* Jean-François Alcover, Jul 26 2011 *)

bb = Array[BellB, n = 25]; s = {}; For[i = 1, i <= n, i++, AppendTo[s, i* bb[[i]] - Sum[s[[d]]*bb[[i-d]], {d, i-1}]]]; Table[Sum[If[Divisible[i, d], MoebiusMu[i/d], 0]*s[[d]], {d, 1, i}]/i, {i, n}] (* Jean-François Alcover, Apr 15 2016 *)

CROSSREFS

Cf. A000110, A305846.

Sequence in context: A273095 A137953 A245893 * A191412 A246013 A219663

Adjacent sequences:  A085683 A085684 A085685 * A085687 A085688 A085689

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 18 2003

STATUS

approved

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Last modified February 26 13:59 EST 2021. Contains 341632 sequences. (Running on oeis4.)