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A290736 Number 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. 2
1, 2, 3, 3, 4, 5, 5, 7, 8, 7, 10, 12, 12, 15, 16, 17, 21, 24, 25, 28, 33, 35, 41, 45, 46, 56, 61, 65, 74, 80, 88, 99, 110, 116, 128, 143, 153, 170, 186, 200, 221, 241, 259, 285, 308, 332, 366, 396, 426, 462, 502, 539, 587, 636, 678, 738, 796, 856, 925, 993 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

George E. Andrews, The Bhargava-Adiga Summation and Partitions, 2016. See (3.4).

FORMULA

See Maple code for g.f.

a(n) ~ exp(Pi*sqrt(n/6)) / (2^(3/2) * sqrt(n)). - Vaclav Kotesovec, May 24 2018

EXAMPLE

For example, the relevant partitions of 7 are 7, 5+1+1, and 1+1+1+1+1+1+1.

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;

D34:=add( q^(2*m+1)*B(-q^2, q^4, m)/(1-q^(4*m+2)), m=0..M):series(D34, q, M); d34seq:=seriestolist(%); BISECT(%, 1);

CROSSREFS

Cf. A008443, A290733-A290739.

Sequence in context: A238746 A272611 A156562 * A007998 A203899 A202704

Adjacent sequences:  A290733 A290734 A290735 * A290737 A290738 A290739

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 10 2017

STATUS

approved

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Last modified February 19 19:28 EST 2020. Contains 332047 sequences. (Running on oeis4.)