A339163 Number of compositions (ordered partitions) of n into distinct parts, the least being 2.

0, 0, 1, 0, 0, 2, 2, 2, 2, 8, 8, 14, 14, 20, 44, 50, 74, 104, 128, 158, 326, 356, 524, 698, 986, 1160, 1592, 2606, 3158, 4316, 5708, 7706, 10082, 12920, 16136, 25718, 30614, 41756, 53396, 71978, 91058, 122144, 149384, 193670, 279614, 342860, 447764, 581234

Offset: 0

Author

Ilya Gutkovskiy, Nov 25 2020

Keywords

• nonn

Examples

			a(9) = 8 because we have [7, 2], [4, 3, 2], [4, 2, 3], [3, 4, 2], [3, 2, 4], [2, 7], [2, 4, 3] and [2, 3, 4].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A002865, A032022, A096749, A339162, A339164, A339165, A339166.

Programs

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-2)*(i+3)/2 `if`(n<2, 0, b(n-2$2, 1)):
seq(a(n), n=0..55);  # Alois P. Heinz, Nov 25 2020

Mathematica

nmax = 47; CoefficientList[Series[Sum[k! x^(k (k + 3)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k! * x^(k*(k + 3)/2) / Product_{j=1..k-1} (1 - x^j).