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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
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 28 2017
STATUS
approved