A282866 Expansion of Product_{k>=1} (1 + k^2*x^(k^2)).

1, 1, 0, 0, 4, 4, 0, 0, 0, 9, 9, 0, 0, 36, 36, 0, 16, 16, 0, 0, 64, 64, 0, 0, 0, 169, 169, 0, 0, 676, 676, 0, 0, 0, 225, 225, 36, 36, 900, 900, 144, 544, 400, 0, 0, 1924, 1924, 0, 0, 1345, 4945, 3600, 576, 772, 14596, 14400, 2304, 2304, 441, 441, 0, 6084, 7848, 1764, 64, 25184, 25120, 0, 256, 3392, 11236, 8100, 0, 576

Offset

0,5

Comments

Sum of products of terms in all partitions of n into distinct squares (A000290).

Links

Table of n, a(n) for n=0..73.

Index entries for related partition-counting sequences

Index entries for sequences related to sums of squares

Formula

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

Example

a(41) = 544 because we have [36, 4, 1], [25, 16], 36*4*1 = 144, 25*16 = 400 and 144 + 400 = 544.

Mathematica

nmax = 73; CoefficientList[Series[Product[1 + k^2 x^k^2, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(PARI) Vec(prod(k=1, 73, (1 + k^2*x^(k^2))) + O(x^73)) \\ Indranil Ghosh, Mar 15 2017

Crossrefs

Cf. A000290, A022629, A033461, A282209.

Sequence in context: A069191 A175362 A189973 * A098445 A290696 A200515

Adjacent sequences: A282863 A282864 A282865 * A282867 A282868 A282869

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2017

Status

approved