A280951 Expansion of Product_{k>=0} 1/(1 - x^(2*k*(k+1)+1)).

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 10, 11, 11, 12, 12, 14, 15, 15, 16, 16, 18, 19, 19, 21, 22, 24, 26, 26, 28, 29, 31, 33, 33, 35, 36, 39, 42, 43, 45, 47, 50, 53, 54, 56, 58, 61, 65, 66, 69, 72, 76, 81, 83, 86, 89, 93, 98, 100, 103, 107, 112, 118, 121, 125, 130, 136, 142, 146

Offset

0,6

Comments

Number of partitions of n into centered square numbers (A001844).

Links

Table of n, a(n) for n=0..82.

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, Centered Square Number

Index entries for sequences related to centered polygonal numbers

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=0} 1/(1 - x^(2*k*(k+1)+1)).

Example

a(10) = 3 because we have [5, 5], [5, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax = 82; CoefficientList[Series[Product[1/(1 - x^(2 k (k + 1) + 1)), {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A001156, A001844, A279220, A280950, A280952, A280953.

Sequence in context: A090735 A090736 A094999 * A120202 A141053 A301507

Adjacent sequences: A280948 A280949 A280950 * A280952 A280953 A280954

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 11 2017

Status

approved