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A290737 Weighted count of partitions of 2n+1 into odd parts in which the largest part appears an odd number of times and all other parts appear twice, with respect to a certain weight. 6
1, 2, 1, 1, 2, -1, 1, 3, -2, 1, 2, 0, 2, 1, 0, -1, 5, 2, -1, 2, -3, 5, 3, -1, 2, 0, 1, 1, 2, -2, 2, 5, 2, -4, 0, 1, -1, 6, 0, 4, -3, -1, 3, -1, 2, 0, 4, -2, 2, 4, -2, 1, 5, -2, -2, -2, 4, 6, 1, 3, -2, 4, -3, -1, -2, 4, 6, 2, 0, -4, 5, 1, 3, -1, 0, 0, 4, -1, -2, 4, -2, 2, 5, 2, 5, -5, -2, 6, -4, 0, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

Andrews (2016), Theorem 2, shows that A008443(n) = A290735(n) + A290737(n) + A290739(n).

LINKS

Table of n, a(n) for n=0..90.

George E. Andrews, The Bhargava-Adiga Summation and Partitions, 2016. See Lemma 3.3.

FORMULA

See Maple code for g.f.

MAPLE

M:=201;

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;

D2:=add( q^(2*m+1)*B(q^2, q^4, m)/(1-q^(4*m+2)), m=0..M):

series(D2, q, M); d2seq:=seriestolist(%); BISECT(%, 1);

CROSSREFS

Cf. A008443, A290733-A290740.

Sequence in context: A322426 A145574 A182579 * A056138 A067594 A089533

Adjacent sequences:  A290734 A290735 A290736 * A290738 A290739 A290740

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Aug 10 2017

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)