A374014 Expansion of (Sum_{k>=0} x^(k^4))^16.

1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 17, 240, 1680, 7280, 21840, 48048, 80080, 102960, 102960, 80080, 48048, 21840, 7280, 1680, 240, 16, 120, 1680, 10920, 43680, 120120, 240240, 360360, 411840, 360360, 240240, 120120, 43680, 10920, 1680, 120, 0

Offset: 0

Author

Seiichi Manyama, Jun 25 2024

Keywords

• nonn

Comments

Number of ways to write n as an ordered sum of 16 fourth powers (A000583).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..20000
• Eric Weisstein's World of Mathematics, Waring's Problem

Crossrefs

Cf. A000583, A002377, A014110, A099591.

Cf. A282288, A374016.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec(sum(k=0, sqrtnint(N, 4), x^k^4)^16)

Formula

a(A099591(n)) = 0.

a(n) > 0 for n > 13792.