OFFSET
0,5
COMMENTS
Partial sums of A111133.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
Riccardo Aragona, Roberto Civino, and Norberto Gavioli, A modular idealizer chain and unrefinability of partitions with repeated parts, arXiv:2301.06347 [math.RA], 2023.
Riccardo Aragona, Roberto Civino, Norberto Gavioli, Carlo Maria Scoppola, A Chain of Normalizers in the Sylow _2-subgroups of the symmetric group on 2^n letters, arXiv:2008.13423 [math.GR], 2020.
Riccardo Aragona, Roberto Civino, Norberto Gavioli, and Carlo Maria Scoppola, Rigid commutators and a normalizer chain, arXiv:2009.11149 [math.GR], 2020.
FORMULA
G.f.: -1/(1 - x)^2 + (1/(1 - x))*Product_{k>=1} 1/(1 - x^(2*k-1)).
a(n) = A036469(n) - n - 1.
a(n) ~ 3^(1/4) * exp(Pi*sqrt(n/3)) / (2*Pi*n^(1/4)). - Vaclav Kotesovec, Aug 21 2018
MAPLE
a:=series(-1/(1-x)^2+(1/(1-x))*mul((1 + x^k), k=1..100), x=0, 53): seq(coeff(a, x, n), n=0..52); # Paolo P. Lava, Apr 02 2019
MATHEMATICA
nmax = 52; CoefficientList[Series[-1/(1 - x)^2 + 1/(1 - x) Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x] (* or *)
nmax = 52; CoefficientList[Series[1/((1 - x) QPochhammer[x, x^2]) - 1/(1 - x)^2, {x, 0, nmax}], x] (* or *)
Table[Sum[PartitionsQ[k] - 1, {k, 0, n}] , {n, 0, 52}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 10 2018
STATUS
approved