A304036 Number of partitions of n into at most 2 copies of 1!, 3 copies of 2!, 4 copies of 3!, ... .

1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 5, 2, 4, 2, 5, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 5, 2, 4, 2, 5, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 5, 2, 4, 2, 5, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Wikipedia, Factorial number system

Formula

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

Example

a(6) = 3 because we have [6], [2,2,2] and [2,2,1,1].

Crossrefs

Cf. A001048, A064986, A303939, A304039.

Sequence in context: A191784 A261350 A259177 * A173442 A112309 A160006

Adjacent sequences: A304033 A304034 A304035 * A304037 A304038 A304039

Keyword

nonn,look

Author

Seiichi Manyama, May 05 2018

Status

approved