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A281542 Expansion of Sum_{i>=1} x^(i^2)/(1 + x^(i^2)) * Product_{j>=1} (1 + x^(j^2)). 3
1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 2, 3, 0, 1, 2, 0, 0, 2, 3, 0, 0, 0, 3, 5, 0, 0, 5, 7, 0, 0, 0, 2, 3, 1, 2, 3, 4, 2, 5, 3, 0, 0, 5, 7, 0, 0, 4, 9, 4, 2, 5, 7, 5, 3, 4, 2, 3, 0, 5, 10, 4, 1, 11, 12, 0, 2, 6, 7, 4, 0, 2, 12, 12, 0, 6, 15, 9, 2, 8, 7, 3, 7, 8, 10, 9, 5, 8, 21, 13, 0, 7, 19, 13, 0, 2, 10, 13, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Total number of parts in all partitions of n into distinct squares.

LINKS

Table of n, a(n) for n=1..100.

Index entries for related partition-counting sequences

FORMULA

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

EXAMPLE

a(26) = 5 because we have [25, 1], [16, 9 ,1] and 2 + 3 = 5.

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Sum[x^i^2/(1 + x^i^2), {i, 1, nmax}] Product[1 + x^j^2, {j, 1, nmax}], {x, 0, nmax}], x]]

CROSSREFS

Cf. A000290, A015723, A033461.

Sequence in context: A025891 A120630 A248509 * A191410 A249142 A225099

Adjacent sequences:  A281539 A281540 A281541 * A281543 A281544 A281545

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 23 2017

STATUS

approved

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)