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

0,6

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to compositions

Formula

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

Example

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].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-2)*(i+3)/2<n, 0,
       add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
    end:
a:= n-> `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]

Crossrefs

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

Sequence in context: A013598 A100943 A152660 * A058787 A353392 A360310

Adjacent sequences: A339160 A339161 A339162 * A339164 A339165 A339166

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 25 2020

Status

approved