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%I #25 Jun 25 2024 13:10:18
%S 1,16,120,560,1820,4368,8008,11440,12870,11440,8008,4368,1820,560,120,
%T 16,17,240,1680,7280,21840,48048,80080,102960,102960,80080,48048,
%U 21840,7280,1680,240,16,120,1680,10920,43680,120120,240240,360360,411840,360360,240240,120120,43680,10920,1680,120,0
%N Expansion of (Sum_{k>=0} x^(k^4))^16.
%C Number of ways to write n as an ordered sum of 16 fourth powers (A000583).
%H Seiichi Manyama, <a href="/A374014/b374014.txt">Table of n, a(n) for n = 0..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Waring's Problem</a>
%F a(A099591(n)) = 0.
%F a(n) > 0 for n > 13792.
%o (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=0, sqrtnint(N, 4), x^k^4)^16)
%Y Cf. A000583, A002377, A014110, A099591.
%Y Cf. A282288, A374016.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jun 25 2024