A339087 Number of compositions (ordered partitions) of n into distinct parts congruent to 4 mod 5.

1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 4, 1, 0, 0, 6, 4, 1, 0, 0, 6, 6, 1, 0, 0, 12, 6, 1, 0, 0, 18, 8, 1, 0, 24, 24, 8, 1, 0, 24, 30, 10, 1, 0, 48, 42, 10, 1, 0, 72, 48, 12, 1, 0, 120, 60, 12, 1, 120, 144, 72, 14, 1, 120, 216, 84, 14, 1, 240

Offset

0,14

Links

Table of n, a(n) for n=0..80.

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(27) = 6 because we have [14, 9, 4], [14, 4, 9], [9, 14, 4], [9, 4, 14], [4, 14, 9] and [4, 9, 14].

Mathematica

nmax = 80; 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. A016897, A017827, A032020, A032021, A109700, A281243, A337547, A337548, A339059, A339060, A339086, A339088, A339089.

Sequence in context: A352245 A227834 A025894 * A051127 A070176 A092606

Adjacent sequences: A339084 A339085 A339086 * A339088 A339089 A339090

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved