OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1 + Sum_{k>=1} (1/(1 - [y^k]P(x,y)) - 1) where P(x,y) = 1/Product_{k>=1} (1 - y*x^k). - Andrew Howroyd, Dec 31 2022
EXAMPLE
The a(0) = 1 through a(4) = 13 sequences:
() ((1)) ((2)) ((3)) ((4))
((11)) ((21)) ((22))
((1)(1)) ((111)) ((31))
((1)(2)) ((211))
((2)(1)) ((1111))
((1)(1)(1)) ((1)(3))
((2)(2))
((3)(1))
((11)(11))
((1)(1)(2))
((1)(2)(1))
((2)(1)(1))
((1)(1)(1)(1))
MATHEMATICA
ptnseq[n_]:=Join@@Table[Tuples[IntegerPartitions/@comp], {comp, Join@@Permutations/@IntegerPartitions[n]}];
Table[Length[Select[ptnseq[n], SameQ@@Length/@#&]], {n, 0, 10}]
PROG
(PARI)
P(n, y) = {1/prod(k=1, n, 1 - y*x^k + O(x*x^n))}
seq(n) = {my(g=P(n, y)); Vec(1 + sum(k=1, n, 1/(1 - polcoef(g, k, y)) - 1))} \\ Andrew Howroyd, Dec 31 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 07 2022
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Dec 31 2022
STATUS
approved