A339235 G.f.: Sum_{k>=0} x^(k^4) / Product_{j=1..k^4} (1 - x^j).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 8, 12, 16, 23, 31, 43, 57, 78, 102, 136, 177, 232, 297, 384, 487, 621, 781, 984, 1226, 1531, 1892, 2340, 2872, 3524, 4294, 5232, 6335, 7666, 9229, 11099, 13288, 15893, 18929, 22519, 26695, 31604, 37293

Offset

0,17

Comments

Number of partitions of n such that the number of parts is a fourth power.

Also number of partitions of n such that the largest part is a fourth power.

Links

Table of n, a(n) for n=0..57.

Index entries for sequences related to partitions

Formula

a(18) = 3 because we have [18], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the first comment) or[16, 2], [16, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the second comment).

Mathematica

nmax = 57; CoefficientList[Series[Sum[x^(k^4)/Product[1 - x^j, {j, 1, k^4}], {k, 0, Floor[nmax^(1/4)] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A000583, A046042, A089333, A334626.

Sequence in context: A318403 A362048 A334626 * A332755 A017912 A102543

Adjacent sequences: A339232 A339233 A339234 * A339236 A339237 A339238

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 05 2020

Status

approved