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A290351
Euler transform of the Bell numbers (A000110).
3
1, 1, 3, 8, 26, 88, 340, 1411, 6417, 31474, 166242, 939646, 5659613, 36158227, 244049562, 1733702757, 12919475840, 100690425442, 818554392962, 6924577964036, 60828588178031, 553821749290234, 5217264062756556, 50776256646839085, 509823607380230570
OFFSET
0,3
LINKS
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*binomial(n-1, j-1), j=1..n))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
b(d), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30);
MATHEMATICA
b[n_]:=b[n]=If[n==0, 1, Sum[b[n - j] Binomial[n - 1, j - 1], {j, n}]]; a[n_]:=a[n]=If[n==0, 1, Sum[Sum[d*b[d], {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