0,3

a(0) = 1 since the only partition of 0 is the empty partition. The product of its terms is the empty product, namely 1.

Same parity as A000009. - Jon Perry (perry(AT)globalnet.co.uk), Feb 12 2004

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. Labelle, personal communication.

T. D. Noe, Table of n, a(n) for n=0..1000

Dean Hickerson, Comments on A006906

The limit of a(n+3)/a(n) is 3. However, the limit of a(n+1)/a(n) does not exist. In fact, the sequence {a(n+1)/a(n)} has three limit points, which are about 1.4422447, 1.4422491 and 1.4422549. - Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 19 2007. See the link below.

a(n) ~ c(n mod 3) 3^(n/3), where c(0)=97923.26765718877..., c(1)=97922.93936857030... and c(2)=97922.90546334208... - Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 19 2007

G.f.: 1 / Product (1-kx^k).

a(n) = (1/n)*Sum_{k=1..n} A078308(k)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 22 2002

Partitions of 0 are {()} whose products are {1} whose sum is 1

Partitions of 1 are {(1)} whose products are {1} whose sum is 1

Partitions of 2 are {(2),(1,1)} whose products are {2,1} whose sum is 3

Partitions of 3 are 3 => {(3),(2,1),(1,1,1)} whose products are {3,2,1} whose sum is 6

Partitions of 4 are {(4),(3,1),(2,2),(2,1,1),(1,1,1,1)} whose products are {4,3,4,2,1} whose sum is 14

(* a[n, k]=sum of products of partitions of n into parts <= k *) a[0, 0]=1; a[n_, 0]:=0; a[n_, k_]:=If[k>n, a[n, n], a[n, k] = a[n, k-1] + k a[n-k, k] ]; a[n_]:=a[n, n] - Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 19 2007

Cf. A007870.

Sequence in context: A026271 A166212 A002219 this_sequence A120940 A049940 A051749

Adjacent sequences: A006903 A006904 A006905 this_sequence A006907 A006908 A006909

nonn,nice,easy

Simon Plouffe (simon.plouffe(AT)gmail.com)

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 04 2001

Edited by N. J. A. Sloane (njas(AT)research.att.com), May 19 2007