A279279 Expansion of Product_{k>=1} (1 + x^(k*(2*k-1))).

1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2

Offset: 0

Author

Ilya Gutkovskiy, Dec 09 2016

Keywords

• nonn

Comments

Number of partitions of n into distinct hexagonal numbers (A000384).

Examples

			a(67) = 2 because we have [66, 1] and [45, 15, 6, 1].
		

Links

• Eric Weisstein's World of Mathematics, Hexagonal Number
• Index to sequences related to polygonal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000384, A024940, A033461, A218380, A278949, A279280, A279281.

Programs

Mathematica

nmax = 120; CoefficientList[Series[Product[1 + x^(k (2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

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