A339169 Number of compositions (ordered partitions) of n into distinct parts, the least being 6.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 56, 62, 86, 116, 140, 170, 218, 248, 296, 350, 518, 572, 764, 938, 1250, 1448, 1880, 2198, 2774, 3212, 3908, 5210, 6146, 7568, 9368, 11750, 14510, 17756, 21476, 26402, 31826, 38432, 45536

Offset

0,14

Links

Table of n, a(n) for n=0..62.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=1} k! * x^(k*(k + 11)/2) / Product_{j=1..k-1} (1 - x^j).

Example

a(21) = 8 because we have [15, 6], [8, 7, 6], [8, 6, 7], [7, 8, 6], [7, 6, 8], [6, 15], [6, 8, 7] and [6, 7, 8].

Mathematica

nmax = 62; CoefficientList[Series[Sum[k! x^(k (k + 11)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A026799, A026827, A339104, A339162, A339163, A339164, A339165, A339166, A339170, A339171, A339172.

Sequence in context: A103795 A123627 A330487 * A171818 A248777 A175101

Adjacent sequences: A339166 A339167 A339168 * A339170 A339171 A339172

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 25 2020

Status

approved