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A279374
Number of ways to choose an odd partition of each part of an odd partition of 2n+1.
16
1, 3, 6, 15, 37, 80, 183, 428, 893, 1944, 4223, 8691, 18128, 37529, 75738, 153460, 308829, 612006, 1211097, 2386016, 4648229, 9042678, 17528035, 33645928, 64508161, 123178953, 233709589, 442583046, 834923483, 1567271495, 2935406996, 5481361193, 10191781534
OFFSET
0,2
COMMENTS
An odd partition is an integer partition of an odd number with an odd number of parts, all of which are odd.
EXAMPLE
The a(3)=15 ways to choose an odd partition of each part of an odd partition of 7 are:
((7)), ((511)), ((331)), ((31111)), ((1111111)), ((5)(1)(1)), ((311)(1)(1)),
((11111)(1)(1)), ((3)(3)(1)), ((3)(111)(1)), ((111)(3)(1)), ((111)(111)(1)),
((3)(1)(1)(1)(1)), ((111)(1)(1)(1)(1)), ((1)(1)(1)(1)(1)(1)(1)).
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(add(d*
[0, 2, 0, 1$4, 2, 0, 2, 1$4, 0, 2][1+irem(d, 16)],
d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, i, t) option remember;
`if`(n=0, t, `if`(i<1, 0, b(n, i-2, t)+
`if`(i>n, 0, b(n-i, i, 1-t)*g((i-1)/2))))
end:
a:= n-> b(2*n+1$2, 0):
seq(a(n), n=0..35); # Alois P. Heinz, Dec 12 2016
MATHEMATICA
nn=20; Table[SeriesCoefficient[Product[1/(1-PartitionsQ[k]x^k), {k, 1, 2n-1, 2}], {x, 0, 2n-1}], {n, nn}]
CROSSREFS
Cf. A000009 (strict partitions), A078408 (odd partitions), A063834, A271619, A279375.
Sequence in context: A370241 A058534 A063778 * A087124 A327647 A086326
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 11 2016
STATUS
approved