A282288 Expansion of (Sum_{k>=0} x^(k^4))^19.

1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 988, 513, 2926, 15505, 58140, 162792, 352716, 604656, 831402, 923780, 831402, 604656, 352716, 162792, 58140, 15504, 3078, 3249, 23275, 116280, 406980, 1058148, 2116296, 3325608, 4157010, 4157010, 3325608

Offset

0,2

Comments

Number of ways to write n as an ordered sum of 19 fourth powers (A000583).

a(n) > 0 for all n >= 0.

Every natural number is the sum of at most 19 fourth powers (Balasubramanian, 1986).

Links

Table of n, a(n) for n=0..42.

Ilya Gutkovskiy, Extended graphical example

Eric Weisstein's World of Mathematics, Biquadratic Number

Eric Weisstein's World of Mathematics, Waring's Problem

Formula

G.f.: (Sum_{k>=0} x^(k^4))^19.

Mathematica

nmax = 42; CoefficientList[Series[Sum[x^k^4, {k, 0, nmax}]^19, {x, 0, nmax}], x]

Crossrefs

Cf. A000583, A002377, A002804, A014110, A173682.

Sequence in context: A224935 A047644 A010935 * A022614 A322878 A060222

Adjacent sequences: A282285 A282286 A282287 * A282289 A282290 A282291

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2017

Status

approved