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);
MATHEMATICA
M = 121;
B[a_, q_, n_] := Module[{j, t1 = 1}, For[j = 0, j <= M, j++, t1 = t1(1 - a q^j)/(1 - a q^(n+j))]; t1];
seq = Sum[q^(2m+1) B[-q^2, q^4, m]/(1 - q^(4m+2)), {m, 0, M}] + O[q]^M // CoefficientList[#, q]& // Partition[#, 2]& // #[[All, 2]]& (* Jean-François Alcover, Dec 16 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 10 2017
STATUS
approved