A294373 Product of first n Bell numbers.

1, 1, 2, 10, 150, 7800, 1583400, 1388641800, 5748977052000, 121573617718644000, 14099500314919737900000, 9567497928695086546803000000, 40313580569855830588349480391000000, 1114446238307803607782300144651734867000000

Offset: 0

Author

Vaclav Kotesovec, Oct 29 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..49

Crossrefs

Cf. A000110, A003266, A070825, A003046, A058807, A058808, A342166, A342170.

Programs

Maple

B:= map(combinat:-bell, [$0..19]):
map(i -> convert(B[1..i],`*`),[$1..20]); # Robert Israel, Oct 29 2017

Mathematica

Table[Product[BellB[k], {k, 0, n}], {n, 0, 15}]

Formula

log(a(n)) ~ n^2 * LambertW(n)/2 * (1 - 3/(2*LambertW(n)) + 3/(2*LambertW(n)^2) + 1/(4*LambertW(n)^3)). - Vaclav Kotesovec, Feb 26 2021