A284836 Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j=1..i} 1/(1 - x^(j^2)).

1, 2, 3, 5, 6, 7, 8, 11, 13, 14, 15, 19, 21, 22, 23, 29, 31, 34, 35, 42, 44, 47, 48, 56, 60, 63, 67, 76, 80, 83, 87, 99, 103, 108, 112, 130, 134, 139, 143, 162, 169, 174, 180, 200, 213, 218, 224, 248, 262, 272, 278, 306, 320, 337, 343, 372, 390, 408, 419, 449, 471, 489, 508, 544, 567, 591, 611, 654, 677, 705

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..70.

Index entries for related partition-counting sequences

Formula

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

Example

a(9) = 13 because we have [9], [4, 4, 1], [4, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 2 + 1 + 9 = 13.

Mathematica

nmax = 70; Rest[CoefficientList[Series[Sum[x^i^2/(1 - x^i^2) Product[1/(1 - x^j^2), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]

Prog

(PARI) x='x+O('x^71); Vec(sum(i=1, 71, x^(i^2)/(1 - x^(i^2)) * prod(j=1, i, 1/(1 - x^(j^2))))) \\ Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A000290, A001156, A046746, A092311, A281541, A284830.

Sequence in context: A140661 A063966 A123030 * A267300 A063752 A191893

Adjacent sequences: A284833 A284834 A284835 * A284837 A284838 A284839

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved