OFFSET
0,11
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)
FORMULA
G.f.: Product_{k>0} (1+x^k)^(A038548(k)-1). - Vaclav Kotesovec, Aug 19 2019
G.f.: Product_{i>=1} Product_{j=2..i} (1 + x^(i*j)). - Ilya Gutkovskiy, Sep 23 2019
EXAMPLE
a(0) = 1: 0 = the empty sum.
a(1) = a(2) = a(3) = 0: no product is < 4.
a(4) = 1: 4 = 2*2.
a(6) = 1: 6 = 2*3.
a(8) = 1: 8 = 2*4.
a(9) = 1: 9 = 3*3.
a(10) = 2: 10 = 2*2 + 2*3 = 2*5.
a(12) = 3: 12 = 2*2 + 2*4 = 2*6 = 3*4.
a(16) = 5: 16 = 2*2 + 2*6 = 2*2 + 3*4 = 2*3 + 2*5 = 2*8 = 4*4.
MAPLE
with(numtheory):
b:= proc(n, i) option remember; local c;
c:= ceil(tau(i)/2)-1;
`if`(n=0, 1, `if`(i<2, 0, b(n, i-1)
+add(b(n-i*j, i-1) *binomial(c, j), j=1..min(c, n/i))))
end:
a:= n-> b(n, n):
seq(a(n), n=0..70);
MATHEMATICA
b[n_, i_] := b[n, i] = Module[{c}, c = Ceiling[DivisorSigma[0, i]/2]-1; If[n==0, 1, If[i<2, 0, b[n, i-1]+Sum[b[n-i*j, i-1]*Binomial[c, j], {j, 1, Min[c, n/i]}]]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Feb 19 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 22 2012
STATUS
approved