A279224 Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)*(2*k-1)/2)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 24, 24, 26, 26, 26, 27, 27, 27, 28, 29, 29, 31, 32

Offset

0,10

Comments

Number of partitions of n into nonzero octagonal pyramidal numbers (A002414).

Links

Table of n, a(n) for n=0..100.

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]

Index to sequences related to pyramidal numbers

Index entries for related partition-counting sequences

Formula

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

Example

a(10) = 2 because we have [9, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax=100; CoefficientList[Series[Product[1/(1 - x^(k (k + 1) (2 k - 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A002414, A068980, A279220, A279221, A279222, A279223.

Sequence in context: A343609 A054898 A279951 * A167383 A167661 A187187

Adjacent sequences: A279221 A279222 A279223 * A279225 A279226 A279227

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 08 2016

Status

approved