OFFSET
0,3
COMMENTS
A twice-partition of n is a sequence of integer partitions, one of each part of an integer partition of n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
EXAMPLE
The a(1) = 1 through a(4) = 14 twice-partitions:
(1) (2) (3) (4)
(11) (21) (22)
(1)(1) (111) (31)
(2)(1) (211)
(11)(1) (1111)
(1)(1)(1) (2)(2)
(3)(1)
(11)(2)
(21)(1)
(11)(11)
(111)(1)
(2)(1)(1)
(11)(1)(1)
(1)(1)(1)(1)
MATHEMATICA
twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn], {ptn, IntegerPartitions[n]}];
Table[Length[Select[twiptn[n], GreaterEqual@@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=Vec(P(n, y)-1), v=[1]); for(k=1, n, my(p=g[k], u=v); v=vector(k+1); v[1] = 1 + O(x*x^n); for(j=1, k, v[1+j] = (v[j] + if(j<k, u[1+j] - u[j]))/(1 - polcoef(p, j)*x^k))); Vec(v[1+n])} \\ Andrew Howroyd, Dec 31 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 03 2022
EXTENSIONS
Terms a(26) and beyond from Andrew Howroyd, Dec 31 2022
STATUS
approved