A302836 a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^(k^2)).

1, 1, 4, 27, 260, 3150, 46872, 825944, 16810048, 387952668, 10010010100, 285526191874, 8921263237056, 303013028232642, 11116057874586840, 438023675344410000, 18451248777413066768, 827408674110381669305, 39353155876513869320412, 1978708139249503877752798

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Index entries for sequences related to partitions

Index entries for sequences related to sums of squares

Formula

a(n) ~ n^n * (1 + 1/n^3 + 1/n^6 + 1/n^8 + 1/n^9 + 1/n^11 + 1/n^12 + 1/n^14 + 2/n^15 + 1/n^16 + 1/n^17 + 2/n^18 + 1/n^19 + 1/n^20 + 2/n^21 + 1/n^22 + 2/n^23 + 4/n^24 + 1/n^25 + 2/n^26 + 4/n^27 + 1/n^28 + 2/n^29 + 5/n^30 + ...), for coefficients see A111178. - Vaclav Kotesovec, Apr 13 2018

Mathematica

Table[SeriesCoefficient[Product[1/(1 - n x^k^2), {k, 1, n}], {x, 0, n}], {n, 0, 19}]

Crossrefs

Cf. A001156, A124577, A285245, A291583, A292417, A300974.

Sequence in context: A360032 A360833 A360835 * A301335 A362701 A177379

Adjacent sequences: A302833 A302834 A302835 * A302837 A302838 A302839

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 13 2018

Status

approved