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A281541 Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) / Product_{j>=1} (1 - x^(j^2)). 8
1, 2, 3, 5, 7, 9, 11, 15, 19, 23, 27, 34, 41, 47, 53, 64, 75, 86, 96, 113, 129, 145, 159, 182, 206, 229, 252, 284, 318, 349, 380, 423, 468, 513, 555, 616, 676, 736, 791, 869, 949, 1026, 1103, 1202, 1310, 1408, 1506, 1631, 1766, 1896, 2020, 2185, 2354, 2525, 2680, 2882, 3094, 3305, 3506, 3751, 4023, 4281, 4537 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Convolution of A001156 and A046951.

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)).

a(n) = Sum_{k=1..n} k * A243148(n,k). - Alois P. Heinz, Sep 19 2018

EXAMPLE

a(8) = 15 because we have [4, 4], [4, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1] and 2 + 5 + 8 = 15.

MAPLE

b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n], (s->

      `if`(s>n, 0, (p->p+[0, p[1]])(b(n-s, i))))(i^2)+b(n, i-1))

    end:

a:= n-> b(n, isqrt(n))[2]:

seq(a(n), n=1..70);  # Alois P. Heinz, Sep 19 2018

MATHEMATICA

nmax = 63; 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, A001156, A006128, A046951, A243148.

Sequence in context: A228121 A323648 A238526 * A066824 A036963 A120431

Adjacent sequences:  A281538 A281539 A281540 * A281542 A281543 A281544

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 23 2017

STATUS

approved

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Last modified August 18 13:25 EDT 2019. Contains 326100 sequences. (Running on oeis4.)