A279222 Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)*(4*k-1)/6)).

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 13, 15, 16, 16, 16, 16, 16, 17, 19, 20, 20, 20, 20, 20, 21, 23, 24, 25, 25, 25, 25, 26, 28, 30, 31, 31, 31, 31, 32, 34, 36, 37, 37, 37, 37, 38, 40, 42, 43, 44, 44, 44

Offset: 0

Author

Ilya Gutkovskiy, Dec 08 2016

Keywords

• nonn

Comments

Number of partitions of n into nonzero hexagonal pyramidal numbers (A002412).

Examples

			a(8) = 2 because we have [7, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
		

Links

• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• Eric Weisstein's World of Mathematics, Hexagonal Pyramidal Number
• Index to sequences related to pyramidal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A002412, A068980, A279220, A279221, A279223, A279224.

Programs

Mathematica

nmax=90; CoefficientList[Series[Product[1/(1 - x^(k (k + 1) (4 k - 1)/6)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)*(4*k-1)/6)).