A328301 Expansion of Product_{k>0} 1/(1 - x^(k^k)).
1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 9, 9, 9, 10, 11, 11, 11, 12, 13, 13, 13, 14, 15, 15, 15, 16, 17, 17, 17, 18, 19, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 39, 39
Offset: 0
Keywords
Examples
G.f.: 1 + x/(1-x) + x^4/((1-x)*(1-x^4)) + x^27/((1-x)*(1-x^4)*(1-x^27)) + ... .
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..10000
Programs
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Maple
b:= proc(n, i) option remember; `if`(n=0 or i=1, 1, b(n, i-1)+(p-> `if`(p>n, 0, b(n-p, i)))(i^i)) end: a:= n-> `if`(n<2, 1, b(n, floor((t-> t/LambertW(t))(log(n))))): seq(a(n), n=0..100); # Alois P. Heinz, Oct 12 2019 -
Mathematica
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, 1, b[n, i - 1] + With[{p = i^i}, If[p > n, 0, b[n - p, i]]]]; a[n_] := If[n < 2, 1, b[n, Floor[PowerExpand[Log[n]/ProductLog[Log[n]]]]]]; a /@ Range[0, 100] (* Jean-François Alcover, Mar 12 2021, after Alois P. Heinz *) -
PARI
my(N=99, x='x+O('x^N)); m=1; while(N>=m^m, m++); Vec(1/prod(k=1, m-1, 1-x^k^k))
Formula
G.f.: 1 + Sum_{n>0} x^(n^n) / Product_{k=1..n} (1 - x^(k^k)).
Comments