A284830 Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j>=i} 1/(1 - x^(j^2)).

1, 2, 3, 5, 6, 8, 10, 14, 16, 19, 23, 30, 33, 38, 44, 55, 60, 69, 77, 93, 102, 113, 126, 148, 162, 177, 198, 226, 246, 268, 293, 334, 361, 392, 424, 480, 516, 556, 601, 668, 721, 773, 835, 917, 990, 1054, 1129, 1239, 1325, 1415, 1508, 1649, 1757, 1875, 1990, 2157, 2303, 2441, 2595, 2796

Offset

1,2

Comments

Total number of smallest parts in all partitions of n into squares (A000290).

Links

Table of n, a(n) for n=1..60.

Index entries for related partition-counting sequences

Formula

G.f.: Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j>=i} 1/(1 - x^(j^2)).

Example

a(9) = 16 because we have [9], [4, 4, 1], [4, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 1 + 5 + 9 = 16.

Mathematica

nmax = 60; Rest[CoefficientList[Series[Sum[x^i^2/(1 - x^i^2) Product[1/(1 - x^j^2), {j, i, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]]

Prog

(PARI) x='x+O('x^61); Vec(sum(i=1, 60, x^i^2/(1 - x^i^2) * prod(j=i, 60, 1/(1 - x^j^2)))) \\ Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A000290, A001156, A092268, A092269, A195820, A281541.

Sequence in context: A056837 A001971 A122493 * A053873 A332272 A240314

Adjacent sequences: A284827 A284828 A284829 * A284831 A284832 A284833

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved