login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258325 a(n) = Product_{k=1..n} (1 + p(k)), where p(k) is the partition function A000041. 3
1, 2, 6, 24, 144, 1152, 13824, 221184, 5087232, 157704192, 6781280256, 386532974592, 30149572018176, 3075256345853952, 418234863036137472, 74027570757396332544, 17174396415715949150208, 5117970131883352846761984, 1975536470906974198850125824 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

Vaclav Kotesovec, The partition factorial constant and asymptotics of the sequence A058694

FORMULA

a(n) ~ c * A058694(n), where c = Product_{k>=1} (1 + 1/p(k)) = 7.60150293364724365227288154074110141857580676049277152624021470033199348...

MAPLE

a:= proc(n) option remember: `if`(n<1, 1,

      (1+combinat[numbpart](n))*a(n-1))

    end:

seq(a(n), n=0..20);

MATHEMATICA

Table[Product[PartitionsP[k]+1, {k, 1, n}], {n, 0, 20}]

CROSSREFS

Cf. A000041, A058694, A078506, A082480.

Sequence in context: A013068 A205182 A326780 * A191006 A082471 A275594

Adjacent sequences:  A258322 A258323 A258324 * A258326 A258327 A258328

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jul 19 2015

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jul 26 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 07:37 EDT 2020. Contains 336368 sequences. (Running on oeis4.)