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A353689
Convolution of A000716 and the positive integers.
1
1, 5, 18, 53, 139, 333, 748, 1592, 3246, 6379, 12152, 22524, 40764, 72213, 125505, 214378, 360473, 597450, 977196, 1578852, 2522157, 3986658, 6239619, 9675801, 14874445, 22679693, 34314378, 51539173, 76875314, 113913453, 167741728, 245534597, 357361857, 517293186
OFFSET
0,2
FORMULA
From Vaclav Kotesovec, May 11 2022: (Start)
G.f.: 1/(1-x)^2 * Product_{k>=1} 1/(1-x^k)^3.
a(n) ~ exp(Pi*sqrt(2*n)) / (2^(5/2) * Pi^2 * sqrt(n)). (End)
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*(2+3*numtheory[sigma](j)), j=1..n)/n)
end:
seq(a(n), n=0..35); # Alois P. Heinz, May 11 2022
MATHEMATICA
nmax = 35; CoefficientList[Series[1/(1 - x)^2 * Product[1/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 11 2022 *)
PROG
(PARI) lista(nn) = Vec(1/(eta('x+O('x^nn))^3*(1-x)^2)); \\ Michel Marcus, May 09 2022
CROSSREFS
Partial sums of A210843.
Column 1 of A353690.
Sequence in context: A226903 A056782 A178684 * A271771 A270990 A272558
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 08 2022
STATUS
approved