login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026007 Expansion of prod(m>=1, (1+q^m)^m ); number of partitions of n into distinct parts, where n different parts of size n are available. 4
1, 1, 2, 5, 8, 16, 28, 49, 83, 142, 235, 385, 627, 1004, 1599, 2521, 3940, 6111, 9421, 14409, 21916, 33134, 49808, 74484, 110837, 164132, 241960, 355169, 519158, 755894, 1096411, 1584519, 2281926, 3275276, 4685731, 6682699, 9501979, 13471239, 19044780, 26850921, 37756561, 52955699 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equals A000219: (1, 1, 3, 6, 13, 24, 48, 86,...) convolved with the aerated version of the latter: (1, 0, 1, 0, 3, 0, 6, 0, 13,...). - Gary W. Adamson, Jun 13 2009

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 1/n*Sum_{k=1..n} A078306(k)*a(n-k). - Vladeta Jovovic, Nov 22 2002

G.f. Product_{m=1}^{infinity} (1+x^m)^m. Weighout transform of natural numbers (A000027). Euler transform of A026741. - Franklin T. Adams-Watters, Mar 16 2006

EXAMPLE

For n = 4, we have 8 partitions

01: [4]

02: [4']

03: [4'']

04: [4''']

05: [3, 1]

06: [3', 1]

07: [3'', 1]

08: [2, 2']

MAPLE

with(numtheory):

b:= proc(n) option remember;

      add((-1)^(n/d+1)*d^2, d=divisors(n))

    end:

a:= proc(n) option remember;

      `if`(n=0, 1, add(b(k)*a(n-k), k=1..n)/n)

    end:

seq(a(n), n=0..45);  # Alois P. Heinz, Aug 03 2013

MATHEMATICA

a[n_] := a[n] = 1/n*Sum[Sum[(-1)^(k/d+1)*d^2, {d, Divisors[k]}]*a[n-k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 41}] (* Jean-Fran├žois Alcover, Apr 17 2014, after Vladeta Jovovic *)

PROG

(PARI)

N=66; q='q+O('q^N);

gf= prod(n=1, N, (1+q^n)^n );

Vec(gf)

/* Joerg Arndt, Oct 06 2012 */

CROSSREFS

Cf. A000009, A000219, A000027, A026741.

Cf. A000219 [From Gary W. Adamson, Jun 13 2009]

Sequence in context: A137685 A169826 A093065 * A032233 A026530 A032254

Adjacent sequences:  A026004 A026005 A026006 * A026008 A026009 A026010

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 24 20:38 EST 2014. Contains 249919 sequences.