OFFSET
0,6
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: (Product_{k>0} 1/(1-q^k)) * B(q), where B(q) is the g.f. of A395257.
a(n) ~ 3*n^(3/2) * exp(Pi*sqrt(2*n/3)) / (5*2^(5/2)*Pi^5). - Vaclav Kotesovec, May 20 2026
MATHEMATICA
nmax = 50; With[{k = 3}, colk = CoefficientList[Series[Sum[(-1)^(i-1) * x^(i*(i-1)/2 + k)/Product[(1 - x^j), {j, 1, 2*k - i}], {i, 1, 2*k} ], {x, 0, nmax}], x]]; Table[Sum[colk[[k+1]]*PartitionsP[n-k], {k, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, May 20 2026 *)
PROG
(PARI) my(N=50, q='q+O('q^N)); concat([0, 0, 0], Vec(1/prod(k=1, N, 1-q^k)*sum(j=1, 6, (-1)^(j-1)*q^(j*(j-1)/2+3)/prod(k=1, 6-j, 1-q^k))))
CROSSREFS
KEYWORD
nonn,new
AUTHOR
Seiichi Manyama, May 17 2026
STATUS
approved
