A341773 Number of partitions of 2*n into exactly n nonzero tetrahedral numbers.

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 4, 2, 0, 4, 2, 0, 4, 3, 0, 5, 4, 1, 5, 4, 1, 5, 5, 1, 6, 6, 2, 6, 6, 2, 6, 7, 3, 7, 9, 4, 8, 9, 4, 8, 10, 5, 9, 12, 6, 10, 12, 7, 10, 13, 8, 12, 15, 10, 13, 16, 11, 13, 17, 12

Offset

0,10

Links

David A. Corneth, Table of n, a(n) for n = 0..2999

Formula

G.f.: Product_{k>=0} 1 / (1 - x^(binomial(k+4,3)-1)).

Mathematica

nmax = 80; CoefficientList[Series[Product[1/(1 - x^(Binomial[k + 4, 3] - 1)), {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000292, A024692, A062748, A068980, A298269, A319799, A338586, A341774, A341775, A341776, A341777, A341778.

Sequence in context: A341791 A341792 A341793 * A359288 A096142 A216921

Adjacent sequences: A341770 A341771 A341772 * A341774 A341775 A341776

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2021

Status

approved