A290352 Euler transform of the Fubini numbers (ordered Bell numbers, A000670).

1, 1, 4, 17, 98, 678, 5687, 55656, 626161, 7963511, 113027113, 1770785023, 30346490633, 564546034917, 11327726548719, 243811768229012, 5602495216123312, 136878883607160468, 3542830077444873188, 96835203745704714722, 2787051847418347608600

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!, m*b(n-1, m)+b(n-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: A353546 A024052 A128321 * A091635 A306160 A127676

Adjacent sequences: A290349 A290350 A290351 * A290353 A290354 A290355

Keyword

nonn

Author

Alois P. Heinz, Jul 28 2017

Status

approved