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A321239 a(n) = [x^(n^3)] Product_{k=1..n} Sum_{m>=0} x^(k^2*m). 1
1, 1, 3, 16, 141, 1534, 19111, 262103, 3853373, 59763670, 966945204, 16191250596, 278933800080, 4921604827876, 88627915588351, 1624349874930925, 30231112607904743, 570284342486800214, 10887435073866747752, 210086404047975194316, 4092940691144348506396, 80432925119259253535963 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of nonnegative integer solutions (a_1, a_2, ... , a_n) to the equation 1^2*a_1 + 2^2*a_2 + ... + n^2*a_n = n^3.

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

1^2* 0 + 2^2*0 + 3^2*3 = 27.

1^2* 1 + 2^2*2 + 3^2*2 = 27.

1^2* 2 + 2^2*4 + 3^2*1 = 27.

1^2* 3 + 2^2*6 + 3^2*0 = 27.

1^2* 5 + 2^2*1 + 3^2*2 = 27.

1^2* 6 + 2^2*3 + 3^2*1 = 27.

1^2* 7 + 2^2*5 + 3^2*0 = 27.

1^2* 9 + 2^2*0 + 3^2*2 = 27.

1^2*10 + 2^2*2 + 3^2*1 = 27.

1^2*11 + 2^2*4 + 3^2*0 = 27.

1^2*14 + 2^2*1 + 3^2*1 = 27.

1^2*15 + 2^2*3 + 3^2*0 = 27.

1^2*18 + 2^2*0 + 3^2*1 = 27.

1^2*19 + 2^2*2 + 3^2*0 = 27.

1^2*23 + 2^2*1 + 3^2*0 = 27.

1^2*27 + 2^2*0 + 3^2*0 = 27.

So a(3) = 16.

PROG

(PARI) {a(n) = polcoeff(prod(i=1, n, sum(j=0, n^3\i^2, x^(i^2*j)+x*O(x^(n^3)))), n^3)}

CROSSREFS

Cf. A001156, A321238.

Sequence in context: A002719 A020554 A062874 * A349969 A109398 A294003

Adjacent sequences: A321236 A321237 A321238 * A321240 A321241 A321242

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 01 2018

STATUS

approved

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Last modified February 7 06:02 EST 2023. Contains 360112 sequences. (Running on oeis4.)