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A290352 Euler transform of the Fubini numbers (ordered Bell numbers, A000670). 4
1, 1, 4, 17, 98, 678, 5687, 55656, 626161, 7963511, 113027113, 1770785023, 30346490633, 564546034917, 11327726548719, 243811768229012, 5602495216123312, 136878883607160468, 3542830077444873188, 96835203745704714722, 2787051847418347608600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..424

FORMULA

a(n) ~ n! / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, May 31 2019

MAPLE

b:= proc(n, m) option remember; `if`(n=0, m!,

      add(b(n-1, max(m, j)), j=1..m+1))

    end:

a:= proc(n) option remember; `if`(n=0, 1, add(add(d*

      b(d, 0), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..30);

MATHEMATICA

b[n_, m_]:=b[n, m]=If[n==0, m!, Sum[b[n - 1, Max[m, j]], {j, m + 1}]]; a[n_]:=a[n]=If[n==0, 1, Sum[Sum[d*b[d, 0], {d, Divisors[j]}] a[n - j], {j, n}]/n]; Table[a[n], {n, 0, 50}] (* Indranil Ghosh, Jul 28 2017, after Maple code *)

CROSSREFS

Cf. A000670, A007003, A095993, A290351.

Sequence in context: A249078 A024052 A128321 * A091635 A306160 A127676

Adjacent sequences:  A290349 A290350 A290351 * A290353 A290354 A290355

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 28 2017

STATUS

approved

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Last modified October 15 21:17 EDT 2019. Contains 328038 sequences. (Running on oeis4.)