A331980 Number of compositions (ordered partitions) of n into distinct odd parts > 1.

1, 0, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 4, 1, 4, 7, 6, 7, 6, 13, 8, 19, 8, 25, 34, 31, 34, 43, 60, 49, 84, 61, 134, 73, 158, 205, 232, 217, 280, 355, 378, 487, 450, 745, 572, 1003, 668, 1381, 1558, 1759, 1678, 2383, 2592, 3001, 3480, 3865, 5162, 4729, 6794, 5953, 9964

Offset: 0

Author

Ilya Gutkovskiy, Feb 03 2020

Keywords

• nonn

Examples

			a(12) = 4 because we have [9, 3], [7, 5], [5, 7] and [3, 9].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A000931, A027349, A032020, A032021, A032022, A087897.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[k! x^(k (k + 2))/Product[(1 - x^(2 j)), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(k + 2)) / Product_{j=1..k} (1 - x^(2*j)).