1,2

Stirling transform of A143463.

Thomas Wieder, Home Page.

Thomas Wieder, (Old) Home Page.

E.g.f: (1/exp(1)) exp( 1 / prod_{k=1}^{inf} (1 - (exp(x)-1)^k / k!) ).

a(n) = sum_{k=1}^{n} C(n-1,k-1) A140585(k) a(n-k).

With S2(n,k) as the Stirling number of the second kind we have

a(n) = sum_{k=1}^{n} A143463(n) S2(n,k).

with (numtheory): with (combinat): b:= proc(k) option remember; add (d/d!^(k/d), d=divisors(k)) end: c:= proc(n) option remember; `if` (n=0, 1, add ((n-1)!/ (n-k)!* b(k)* c(n-k), k=1..n)) end: aa:= n-> add (stirling2 (n, k) * c(k), k=1..n): a:= proc(n) option remember; `if` (n=0, 1, aa(n)+ add (binomial (n-1, k-1) *aa(k) *a(n-k), k=1..n-1)) end: seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008]

A140585, A143463.

Sequence in context: A049377 A129890 A120733 this_sequence A001828 A084845 A098460

Adjacent sequences: A144789 A144790 A144791 this_sequence A144793 A144794 A144795

nonn

Thomas Wieder (thomas.wieder(AT)t-online.de), Sep 21 2008

More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008