login
A299166
Expansion of 1/(1 - x*Product_{k>=1} 1/(1 - x^k)^k).
10
1, 1, 2, 6, 17, 48, 132, 365, 1003, 2759, 7583, 20843, 57283, 157442, 432719, 1189317, 3268818, 8984318, 24693343, 67869557, 186539251, 512702559, 1409161449, 3873076007, 10645137706, 29258128633, 80415877302, 221022792843, 607480469466, 1669658209311, 4589050472041
OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
FORMULA
G.f.: 1/(1 - x*Product_{k>=1} 1/(1 - x^k)^k).
a(0) = 1; a(n) = Sum_{k=1..n} A000219(k-1)*a(n-k).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, k*add(
b(n-j, k)*numtheory[sigma][2](j), j=1..n)/n)
end:
a:= n-> add(b(n-j, j), j=0..n):
seq(a(n), n=0..35); # Alois P. Heinz, Feb 04 2018
MATHEMATICA
nmax = 30; CoefficientList[Series[1/(1 - x Product[1/(1 - x^k)^k, {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
Antidiagonal sums of A255961.
Sequence in context: A032638 A292229 A090039 * A136776 A018915 A019487
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 04 2018
STATUS
approved