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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A290734 Number of compact partitions of n containing a 1 where each partition is counted with a certain weight. 3
0, -1, 2, -2, 3, -6, 6, -4, 6, -9, 10, -8, 6, -12, 14, -6, 7, -16, 16, -8, 10, -18, 14, -8, 8, -17, 24, -10, 6, -24, 22, -4, 10, -22, 20, -16, 9, -20, 28, -6, 8, -32, 26, -8, 14, -28, 24, -8, 8, -25, 34, -18, 6, -36, 34, -2, 18, -28, 24, -24, 10, -28, 40, -4, 7, -42, 38, -12, 18, -40, 26, -12, 12, -28 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See Andrews (2016) for the definition of the particular weight used here.

4*A290733(n) + 2*A290734(n) = (-1)^n*A005875(n) for n > 0.

LINKS

Table of n, a(n) for n=0..73.

George E. Andrews, The Bhargava-Adiga Summation and Partitions, 2016. See Lemma 2.2.

FORMULA

See Maple program for g.f.

MAPLE

M:=101;

B:=proc(a, q, n) local j, t1; global M;

t1:=1;

for j from 0 to M do

t1:=t1*(1-a*q^j)/(1-a*q^(n+j));

od;

t1; end;

# c_1

T1:=add( (-1)^m*q^(m*(m+1)/2)/(B(-q, q, m)*(1+q^m)), m=1..M):

series(T1, q, M); c1seq:=seriestolist(%);

CROSSREFS

Cf. A005875, A290733.

Sequence in context: A070871 A096115 A289838 * A093919 A179661 A178888

Adjacent sequences:  A290731 A290732 A290733 * A290735 A290736 A290737

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Aug 10 2017

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 March 24 19:48 EDT 2019. Contains 321448 sequences. (Running on oeis4.)