A279280 Expansion of Product_{k>=1} (1 + x^(k*(5*k-3)/2)).

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

Offset: 0

Author

Ilya Gutkovskiy, Dec 09 2016

Keywords

• nonn

Comments

Number of partitions of n into distinct heptagonal numbers (A000566).

Examples

			a(81) = 2 because we have [81] and [55, 18, 7, 1].
		

Links

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

Crossrefs

Cf. A000566, A024940, A033461, A218380, A279012, A279279, A279281.

Programs

Mathematica

nmax = 120; CoefficientList[Series[Product[1 + x^(k (5 k - 3)/2), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 + x^(k*(5*k-3)/2)).