A290573 Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)*(k+2)*(k+3)/24)).

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 12, 12, 12, 12, 12, 16, 16, 16, 16, 16, 20, 20, 20, 20, 20, 25, 25, 25, 25, 25, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 44, 44, 44, 44, 44, 52, 52, 52, 52, 52, 62, 62, 62, 62, 62, 73, 73, 73, 73, 73, 85, 85, 85, 85, 85, 99

Offset: 0

Author

Ilya Gutkovskiy, Aug 15 2017

Keywords

• nonn

Comments

Number of partitions of n into nonzero 4-dimensional pyramidal numbers (A000332).

Examples

			a(10) = 3 because we have [5, 5], [5, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
		

Links

• Index to sequences related to pyramidal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000292, A000332, A007294, A068980, A290792.

Programs

Mathematica

nmax = 85; CoefficientList[Series[Product[1/(1 - x^(k (k + 1) (k + 2) (k + 3)/24)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)*(k+2)*(k+3)/24)).