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Revision History for A046746 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Sum of smallest parts of all partitions of n.
(history; published version)
#100 by Susanna Cuyler at Fri Jun 04 22:52:21 EDT 2021
STATUS

proposed

approved

#99 by Jon E. Schoenfield at Fri Jun 04 21:17:43 EDT 2021
STATUS

editing

proposed

#98 by Jon E. Schoenfield at Fri Jun 04 21:17:41 EDT 2021
COMMENTS

Starting with offset 1, = the partition triangle A026794 * [1, 2, 3, ...]. - Gary W. Adamson, Feb 13 2008

For n >= 1, a(n) = T(n+1,1) + T(n+2,2) + T(n+3,3)+ ... (sum along a falling diagonal) of the partition triangle A026794. - Bob Selcoe, Jun 22 2013

FORMULA

G.f.: Sum_{k>=1} (-1 + 1/Product_{i>=0} (1-z^(k+i))). - Vladeta Jovovic, Jun 22 2003 [Cannot verify, Joerg Arndt, Apr 17 2011]

G.f.: Sum_{j>=1} (x^j/(1-x^j))/Product(1-x^i, _{i=1..j), j=} (1..infinity-x^i). - Vladeta Jovovic, Aug 11 2004 [Cannot verify, Joerg Arndt, Apr 17 2011]

G.f.: sum_Sum_{k >= 1} (-1 + z^k/(1-z^k)(1-z^{k+1})(1-z^{k+2})...). - Don Knuth, Aug 08 2002 [Cannot verify, Joerg Arndt, Apr 17 2011]

G.f.: sum(Sum_{n>=1, } (x^n/(1-x^n) ) / prod(Product_{k=1..n, } (1-x^k) ). - Joerg Arndt, May 26 2012

STATUS

approved

editing

#97 by Alois P. Heinz at Mon Aug 10 02:27:23 EDT 2020
STATUS

editing

approved

#96 by Alois P. Heinz at Mon Aug 10 01:53:20 EDT 2020
CROSSREFS
STATUS

approved

editing

#95 by Vaclav Kotesovec at Sat Jul 06 10:50:33 EDT 2019
STATUS

editing

approved

#94 by Vaclav Kotesovec at Sat Jul 06 10:50:28 EDT 2019
KEYWORD

nonn,changed,nice

STATUS

approved

editing

#93 by OEIS Server at Sat Jul 06 09:52:45 EDT 2019
LINKS

Vaclav Kotesovec, <a href="/A046746/b046746_2.txt">Table of n, a(n) for n = 0..20000</a> (terms 0..10000 from Alois P. Heinz)

#92 by Vaclav Kotesovec at Sat Jul 06 09:52:45 EDT 2019
STATUS

editing

approved

Discussion
Sat Jul 06
09:52
OEIS Server: Installed new b-file as b046746.txt.  Old b-file is now b046746_2.txt.
#91 by Vaclav Kotesovec at Sat Jul 06 09:52:35 EDT 2019
LINKS

Alois P. Heinz, Vaclav Kotesovec, <a href="/A046746/b046746_2.txt">Table of n, a(n) for n = 0..20000</a> (terms 0..10000</a> from Alois P. Heinz)

STATUS

approved

editing