A339086 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 5.

1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 1, 4, 6, 0, 0, 1, 4, 6, 0, 0, 1, 6, 12, 0, 0, 1, 6, 18, 24, 0, 1, 8, 24, 24, 0, 1, 8, 30, 48, 0, 1, 10, 42, 72, 0, 1, 10, 48, 120, 120, 1, 12, 60, 144, 120, 1, 12, 72, 216, 240, 1, 14, 84, 264, 360, 1, 14, 96, 360, 600, 1, 16, 114

Offset

0,8

Links

Table of n, a(n) for n=0..78.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=0} k! * x^(k*(5*k - 3)/2) / Product_{j=1..k} (1 - x^(5*j)).

Example

a(18) = 6 because we have [11, 6, 1], [11, 1, 6], [6, 11, 1], [6, 1, 11], [1, 11, 6] and [1, 6, 11].

Mathematica

nmax = 78; CoefficientList[Series[Sum[k! x^(k (5 k - 3)/2)/Product[1 - x^(5 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A003520, A016861, A032020, A032021, A109697, A280454, A337547, A337548, A339059, A339060, A339087, A339088, A339089.

Sequence in context: A197881 A332712 A079126 * A186336 A025891 A341000

Adjacent sequences: A339083 A339084 A339085 * A339087 A339088 A339089

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved