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

Author

Ilya Gutkovskiy, Feb 12 2017

Keywords

• nonn
• look

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

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Ilya Gutkovskiy, Extended graphical example
• Eric Weisstein's World of Mathematics, Biquadratic Number
• Eric Weisstein's World of Mathematics, Waring's Problem

Crossrefs

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

Programs

Mathematica

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

Formula

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