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A320293
Number of series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of n with no 1's.
3
0, 1, 1, 3, 3, 9, 11, 30, 45, 112, 195, 475, 901, 2136, 4349, 10156, 21565, 50003, 109325, 252761, 563785, 1303296, 2948555, 6826494, 15604053, 36210591, 83415487, 194094257, 449813607, 1049555795, 2444027917, 5718195984, 13367881473, 31357008065, 73546933115
OFFSET
1,4
COMMENTS
Also phylogenetic trees on integer partitions of n with no 1's.
LINKS
EXAMPLE
The a(2) = 1 through a(7) = 11 trees:
(2) (3) (4) (5) (6) (7)
(22) (32) (33) (43)
((2)(2)) ((2)(3)) (42) (52)
(222) (322)
((2)(4)) ((2)(5))
((3)(3)) ((3)(4))
((2)(22)) ((2)(23))
((2)(2)(2)) ((3)(22))
((2)((2)(2))) ((2)(2)(3))
((2)((2)(3)))
((3)((2)(2)))
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(p=1/prod(k=2, n, 1 - x^k + O(x*x^n)), v=vector(n)); for(n=1, n, v[n]=polcoef(p, n) + EulerT(v[1..n])[n]); v} \\ Andrew Howroyd, Oct 25 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 09 2018
EXTENSIONS
Terms a(23) and beyond from Andrew Howroyd, Oct 25 2018
STATUS
approved