A281542 - OEIS

A281542

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

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

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OFFSET

1,5

COMMENTS

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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)).

From Alois P. Heinz, Feb 03 2021: (Start)

a(n) = Sum_{k>=0} k * A341040(n,k).